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OF  THE 


UNIVERSITY  OF  CALIFORNIA 


GIFT  OF" 


Class 


UNIVERSITY  OF  CALIFORNIA  PUBLICATIONS 


Determination  of  The  Constant  of 
Refraction  from  Observations  made 
with  The  Repsold  Meridian  Circle 
of  The  Lick  Observatory 


DISSERTATION    IN    PARTIAL    FULFILLMENT   OF   THE    REQUIREMENTS    FOR   THE 

DEGREE  OF   DOCTOR  OF    PHILOSOPHY  IN  THE  UNIVERSITY  OF   CALIFORNIA 

PRESENTED    IN    IQOI    BY 


RUSSELL    TRACY    CRAWFORD 


[Reprinted   from  the  Proceedings  of  the  California  Academy  of  Sciences, 
Third  Series;  Math.-Physics;  Vol.  I,  No.  8.] 


DETERMINATION  OF  THE  CONSTANT  OF  REFRACTION 

FROM     OBSERVATIONS     MADE    WITH     THE 

REPSOLD    MERIDIAN   CIRCLE  OF  THE 

LICK    OBSERVATORY. 


BY    RUSSEI.L    TRACY    CRAWFORD. 

OF  THE 

UNIVERSITY 


CONTENTS. 

PAGE. 

INTRODUCTION . .  - . 105 

1.  The  Meridian  Circle 105 

2.  The  Room 107 

j.     Meteorology 108 

4.     Plan  for  Observing 114 

OBSERVATIONS 1 18 

/.     List 118 

2.     Details  of  Observations 119 

j.     Reduction  of  Observations 122 

4.     The  Cons/ant  of  Refraction 190 

j.     Latitude 191 

CONCLUSION 192 

ADDENDUM 193 

INTRODUCTION. 

i.  The  Meridian  Circle. — The  instrument  with  which 
these  observations  for  refraction  were  made  has  been  fully 
described  by  Astronomer  Tucker  in  Volume  IV  of  the 
"  Publications  of  the  Lick  Observatory,  1900."  For  the 
sake  of  completeness,  however,  it  will  be  described  again 
in  this  paper. 

The  instrument  was  made  by  Messrs.  Repsold  and  Sons, 
and  was  described  by  Professors  Auwers  and  Krueger  to  be 
"  in  its  construction  in  every  way  suited  to  be  the  chief 
instrument  in  an  observatory  of  the  first  class/'  (cf.  Vol.  I, 
"  Publications  of  the  Lick  Observatory.") 

The  aperture  of  the  object  glass,  which  was  made  by 
Clark  and  Sons,  is  6.4  inches.  Its  focal  length  is  6  feet 


IO6  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  3D  SER. 

4  inches.  The  tube  of  the  telescope  is  in  two  parts,  each 
of  which  is  attached  to  a  central  cube.  Their  diameters 
decrease  from  8.1  inches  at  the  cube  to  6.5  inches  near 
their  outer  ends.  An  eyepiece  giving  a  power  of  90  and  a 
field  of  12'  was  used  for  these  observations.  The  star 
images  formed  are  not  exactly  round,  but  are  slightly  elon- 
gated in  a  direction  parallel  to  the  horizontal  (declination) 
thread.  There  being  no  component  of  this  elongation 
parallel  to  the  vertical  threads,  it  can  have  no  effect  upon 
observations  for  zenith  distance. 

The  axis  is  3  feet  2^4  inches  long,  the  distance  between 
the  counterpoises  being  2  feet  2  inches.  The  pivots  are 
3.6  inches  in  diameter  and  are  protected  by  brass  covers. 
The  telescope  is  furnished  with  clamps  which,  however, 
were  never  used  during  these  observations.  After  the 
telescope  was  once  set  for  a  star  it  was  not  moved  again  to 
make  the  bisection,  this  being  done  by  means  of  the 
declination  micrometer.  The  value  of  one  revolution  oi 
the  screw  of  this  micrometer  is  48".  10.  This  value  has 
been  adopted  as  the  result  of  many  determinations  made  in 
past  years.  The  micrometer  thread  is  single. 

The  instrument  has  two  circles,  one  of  which  can  be 
rotated  about  the  axis  of  the  instrument  while  the  other  is 
rigidly  fixed  to  it.  They  are  both  graduated  to  2'.  The 
degrees,  as  numbered,  increase  counter-clockwise.  The 
diameter  of  the  silver  circle,  upon  which  the  graduations 
are  marked,  is  26  inches.  There  are  130  graduations  to 
the  inch.  The  fixed  circle  was  used  throughout  these 
observations.  , 

The  four  reading  microscopes  on  each  side  are  alike  in 
all  respects.  They  are  26.5  inches  long  and  have  clear 
aperturqs  of  0.55  of  an  inch.  Their  powers  are  40  and  their 
fields  are  nearly  one  degree.  The  objectives  are  5  inches 
from  the  circle  and  their  eye  ends  project  8  inches  from 
the  frame  holding  them.  The  micrometer  heads  are  divided 
into  60  parts.  One  revolution  of  a  micrometer  head  carries 
the  threads  over:ne  minute  of  arc  of  the  circle.  There 


M.-P.— VOL.  L]     CRAWFORD— CONSTANT  OF  REFRACTION.         107 

are  two  pairs  of  threads  in  every  micrometer,  but  one  of 
which  is  generally  used. 

There  is  a  separate  broken  telescope  for  setting.  This 
is  supported  on  wyes  attached  to  either  pier  and  is  at  the 
level  of  the  lower  rim  of  the  circle.  By  means  of  this  the 
circle  can  be  seen  either  from  the  north  or  from  the  south, 
so  that  the  settings  can  be  made  very  conveniently. 

The  illumination  for  both  the  field  of  view  and  for  the 
circles  under  the  microscopes  is  furnished  by  a  Rochester 
lamp  placed  in  a  cylindrical  case  9  feet  from  the  axis  of  the 
instrument.  This  light  also  illuminates  the  heads  of  the 
microscope  micrometers.  Most  of  the  heat  from  this  lamp 
is  carried  out  of  the  room  by  a  pipe  which  extends  from 
directly  over  the  lamp  through  the  roof  to  the  outside  air. 

A  simple  mechanism  enables  the  observer  to  change  the 
system  of  illumination  from  a  bright  field  with  dark  wires  to 
a  dark  field  with  bright  wires  and  vice  versa;  he  can  also 
reduce  the  amount  of  illumination  at  will. 

The  brick  piers  supporting  the  instrument  are  34  inches 
by  44  inches  at  the  floor  of  the  room  and  22  inches  square 
at  the  top.  The  sides  next  to  the  telescope  are  vertical. 
They  are  cased  in  wood  with  a  layer  of  felt  between  the 
surfaces.  The  platforms  for  the  microscope  reader  are 
entirely  disconnected  from  the  casing  of  the  piers. 

The  microscope  bearers  are  23  inches  in  diameter  and 
17  inches  long.  The  wyes  for  the  pivots  of  the  instrument 
are  attached  to  the  inner  faces  of  these  frames. 

The  weights  of  the  counterpoises  hang  from  levers 
26  inches  long.  The  fulcra  are  in  the  centers  of  the  levers 
and  are  6  inches  from  the  inner  faces  of  the  microscope 
bearers. 

Two  collimators,  of  same  aperture  and  focal  length  as  the 
Meridian  Circle,  are  suitably  mounted.  The  collimator 
micrometers  are  35  feet  6  inches  apart. 

2.  The  Room. — The  Meridian  Circle  house  on  Mount 
Hamilton  has  been  most  admirably  designed.  Its  efficiency 
will  become  apparent  from  the  meteorological  data  to  be 
given  later. 

(2)  May  5,  1903- 


108  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 

The  observing  room  is  43  feet  long  (north  and  south)  and 
38  feet  wide.  All  of  the  walls  are  double.  The  outer  of 
the  two  is  a  louvre-work  of  galvanized  iron  which  prevents 
the  sunlight  from  touching  any  part  of  the  building  proper. 
The  inner  wall  is  of  California  redwood,  and  is  separated 
from  the  outer  by  a  two  foot  air  space.  The  ceiling  is 
also  of  redwood.  It  is  about  16  feet  above  the  floor. 
Above  the  ceiling  is  an  air  space  8  feet  high  at  the  observing 
slit  and  sloping  to  meet  the  east  and  the  west  walls. 

The  observing  slit  is  slightly  over  three  feet  in  width. 
The  covering  for  the  slit  is  in  four  parts  which  open  out- 
ward. The  ends  are  closed  by  shutters,  each  of  which  is 
in  two  parts  opening  inwards.  Each  end  is  also  provided 
with  a  single  shutter  which  slides  up  and  down.  For  stars 
at  zenith  distances  greater  than,  72  degrees  these  shutters 
have  to  be  lifted.  When  down  they  are  very  efficient  wind 
breaks. 

There  is  a  large  canopy  which  can  be  rolled  over  the 
instrument  to  serve  as  an  additional  protection  in  stormy 
weather  or  when  the  instrument  is  not  in  use. 

For  a  more  detailed  account  of  the  instrument  and  room 
see  Astronomer  Tucker's  account  of  them  in  Volume  IV 
of  the  "  Publications  of  the  Lick  Observatory,  1900." 

j.  Meteorology. — To  make  quite  sure  of  the  condition 
of  the  atmosphere  at  any  time  during  the  observations,  the 
thermometers  were  read,  on  the  average,  three  times  an 
hour  (at  nearly  equal  intervals);  and  the  barometer  was 
observed  every  hour.  The  reading  of  the  wet  bulb  ther- 
mometer was  also  taken  when  the  dry  was  read.  The 
relative  humidity  has  not  been  introduced  into  the  reduc- 
tions, but  it  was  thought  desirable  to  have  it  for  possible 
future  reductions. 

The  barometer,  Green  2839,  nangs  on  the  north  wall  of 
the  observing  room.  •  It  reads  to  one  two-hundredth  of  an 
inch.  The  dry  and  the  wet  bulb  thermometers  (F)  hang  in 
the  air  space  between  the  north  walls.  .  The  dry  bulb  ther- 
mometer, used  to  indicate  the  external  temperatures,  is 
Green  494.  This  thermometer  has  been  calibrated  at  the 


M.-P.—  VOL.  I.]     CRAWFORD— CONSTANT  OF  REFRACWON.         109 

Yale  Observatory.  The  corrections  which  have  been 
applied  to  all  the  readings  have  been  taken  from  the 
following  table  sent  from  Yale  Observatory:  — 


/(Fj 

Cor. 

0° 

+o°.i 

32 

Q   w  2 

52:! 

!      —0   .1 

,  N 

j 

112 

j      —0  .  1 

The  table  which  follows  contains  the  unconnected  temper- 
atures (t),  the  readings  of  the  attached  thermometer  (T), 
of  the  barometer  (B),  and  the  times  at  which  they  were 
taken.  The  readings  of  the  wet  bulb  thermometer  are  not 
given  here. 


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M.-P.— VOL.  I.]     C^^  WFORD—  CONST  A  NT  OF  REFRA  CTION,         III 


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112  CA  LIFORNIA  A  CA DEMY  OF  SCIENCES.        [PROC.  30  SER. 

In  this  table  the  unit  of  B  is  one  two-hundredth  of  an 
inch. 

From  this  table  the  following  data  have  been  taken: 

Maximum  temperature  =  74°.  o,  July      3 
Minimum   temperature  =  55°.  i,  June   12     , 
Maximum  range  =  18°. 9 

Maximum  barometer  —  5194,  June  14 
Minimum  barometer  =  5145,  June  12" 
Maximum  range  =  49. 

During  this  period  of  observing,  the  maximum  differ- 
ence .between  the  dry  and  the  wet  bulb  thermometers  was 
75°. 5. —  48°. o  =  22°. 5.  This  was  on  June  29.  The 
minimum  was  65°.  o  —  56°. o  =  9°.o,  which  occurred 
June  27. 

Concerning  the  maximum  temperature  noted  above, 
74°. o,  it  should  be  remarked  that  this  was  the  first  reading 
of  the  period,  and  was  taken  several  minutes  before  the 
sun  had  set. 

Besides  the  regular  thermometers  in  the  air  space  be- 
tween the  north  walls,  three  other  thermometers  were  sus- 
pended from  the  ceiling  of  the  observing  room.  All  three 
were  swung  under  the  observing  slit,  near  the  plane  of 
the  meridian.  One  was  directly  over  the  instrument,  and 
three  or  four  feet  from  the  ceiling.  The  other  two  were 
hung,  one  north  and  one  south,  about  half  way  between 
the  instrument  and  the  north  and  south  walls  respectively, 
and  at  such  a  distance  above  the  floor  that  the  plane  of  the 
axis  of  the  instrument  and  the  line  of  sight  of  the  telescope, 
pointed  at  about  83°  zenith  distance  (north  and  south 
respectively),  would  intersect  the  thermometers  near  their 
bulbs. 

Before  being  thus  placed,  these  thermometers  were 
compared  with  Green  494,  so  that  their  readings  could  be 
reduced  for  comparison  with  those  of  the  external  ther- 
mometer (Green  494). 

During  the  course  of  an  evening's  observations  these 
three  thermometers  were  read  just  after  reading  the  regular 
thermometer.  The  average  difference  between  the  inside 
and  the  outside  thermometers  was  found  to  be  the  same 


M.-P.— VOL.  I.}     CKAWFORD—  CONS7*ANT  OF  REFRACTION.         113 

for  all  three,  and  is  o°.3  (F).  It  is  nearly  always  the  case 
(in  this  hemisphere)  that  the  southern  part  of  a  room  is  a 
trifle  warmer  than  the  northern.  But  this  is  not  the  case 
on  Mount  Hamilton.  The  temperature  of  the  air  inside 
is,  on  the  average,  very  uniform  and  but  very  little  (o°.3) 
warmer  than  the  air  outside.  In  his  "  Untersuchung  liber 
die  Astronomische  Refraction  u.  s.  w.,"  Dr.  Bauschinger 
notes  that  the  southern  part  of  his  observing  room  in 
Munich  was  warmer  than  the  northern,  and  that  at  night 
the  average  difference  between  the  inside  and  the  outside 
temperatures  is  i°-3  (C).  From  his  investigation,  he  con- 
cludes that  the  temperature  of  the  air  within  the  observing 
room  should  be  taken  into  account. 

Because  of  these  difficulties,  many  observers  have  seri- 
ously considered  the  idea  of  mounting  their  instruments 
under  a  movable  house,  so  that  when  at  work  the  instru- 
ment will  be  entirely  out  of  doors,  and  thus  completely 
obviate  this  difficulty.  But  this  would  needlessly  endanger 
the  instrument.  To  accomplish  the  same  purpose,  the 
Meridian  Circle  house  being  built  at  Kiel  is  to  be  con- 
structed in  the  shape  of  a  cylinder  whose  axis  coincides 
with  the  axis  of  the  instrument.  This  is  undoubtedly  the 
best  form  of  construction. 

For  the  efficiency  of  the  Meridian  Circle  house  on  Mount 
Hamilton,  the  difference  between  the  inside  and  the  outside 
thermometers  can  speak.  As  has  been  said,  the  average 
difference  (in  the  sense  Inside-Outside)  is  -\-  o°.3  (F). 
The  maximum  difference  noted  was  one  evening,  a  few 
minutes  before  the  sun  had  set,  when  the  difference 
was.+  i°.i  (F).  The  maximum  difference  noted  here  is 
less  than  half  the  average  at  Munich.  After  this  Meridian 
Circle  house  has  been  completely  opened  for  an  hour  and 
a  half,  the  temperature  inside  is  practically  the  same  as  it  is 
outside. 

During  the  months  October  to  December,  inclusive,  a 
similar  set  of  observations  was  secured.  For  these  months 
the  average  difference  between  the  inside  and  the  outside 
temperatures  is  even  less  than  for  the  summer  months. 
But  the  range  of  the  difference  is  much  greater  for  the 


114  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC,  30  SER. 

fall  and  the  winter  months.  The  maximum  differences 
observed  were  —  2°.o  (  F)  and  -f-  2°.i  (F).  There  was 
one  still  larger  difference,  viz.  —  3°.  7  (F),  which  can 
hardly  be  counted  in  the  series,  for  it  occurred  on  a  poor 
night,  immediately  after  observing  had  been  suspended 
because  of  clouds  and  poor  "seeing."  The  hot  wave, 
which  caused  the  outside  temperature  to  rise  suddenly, 
undoubtedly  destroyed  the  "seeing."  Although  the 
winter  months  present  conditions  not  so  favorable  as  those 
of  the  summer  months,  nevertheless  they  also  speak  well 
for  the  efficiency  of  the  Lick  Observatory  Meridian 
Circle  house. 

^.  Plan  for  Observing.  —  The  method  of  determining 
the  refractions  here  may  be  stated  as  being  a  quasi  con- 
verse to  Talcott's  method  of  determining  the  latitude. 
Instead  of  eliminating  the  refractions  to  get  the  latitude, 
the  method  is  to  determine  the  refractions  by  eliminating 
the  latitude,  as  follows: 
Let 

z8   =  the  zenith  distance  of  a  southern  star, 
zn  =  the  zenith  distance  of  a  northern  star, 
z'g  =  the  apparent  zenith  distance  of  the  southern  star, 
z'n  =  the  apparent  zenith  distance  of  the  northern  star, 
S8   =  the  declination  of  the  southern  star, 
8n  =  the  declination  of  the  northern  star, 
rs    =  the  refraction  of  the  southern  star, 
rn   ==  the  refraction  of  the  northern  star, 
<p    =  the  latitude  of  the  Meridian  Circle. 
Then 

«»=*+*„=?+  (z'n+rn)  (i) 

Ss=?—  z8=v—  (z'8+rs)  (2) 


Let 

A=Sn-Ss  (4) 

B=z's+z'n  (5) 

Then 

A=B  +  rs+rn  (6) 

or 

rs+rn=A—  B  (7) 


M.-P.— VOL.  I.  ]     CRA  WFORD—  CONST  A  NT  OF  RE  PR  A  CTION.          115 

If  now,  the  southern  and  northern  zenith  distances  were 
the  same,  and  if,  at  the  times  of  observing  them,  the  condi- 
tions of  the  atmosphere  were  the  same,  the  two  refractions 
would  be  the  same,  /.  e., 

ra=rn. 
In  this  case  we  have 

2r=A— B  (I) 

In  practice  these  ideal  conditions  are  only  approximately 
satisfied.     We  therefore  proceed  as  follows: 
From  (7)  we  have 

2r8-rs+rn=A-B  (8) 

whence 

2r.=  (A— B)  +  (r—  r.) 
and 

r.  =  #(A— B)  +  #(r.— r,,)) 

also  >-  (II) 

rB=#(A— B)  +  tf(r,,— r.)) 

In  case  the  northern  star  is  at  lower  culmination  we  shall 
have: 

Sn=i8o°— zn— v  (9) 

S8=¥—zs  (10) 

Sn+S.=i8o°_zu— z.  (ii) 

^180°—  [Z'n  +  rn+z'8-fr8].  (12) 

Hence 

rn-+r8=i8o°—  [z'n+z'B] -[«„  +  «.]  (13) 

and 

2r8=  i8o°-[Z'n+Z'8]-[A+  8J+ [r.— rj.    ( 14) 
Calling 

A'=Sn+S8  (15) 

and  since 

B=z'.+z'B  (5) 

we  have 

r8=9o°-^  [A'+B]  +  y2  [r -rD]  ) 

and  >•  (III) 

r»=90°— ^[A'  +  B]  +  ^[rn—  rj  ) 

In  order  to  obtain  the  refractions  from  (II)  and  (III)  it 
is  necessary  to  know  the  declinations  of  the  stars,  their 
apparent  zenith  distances  (or  rather  the  sums  of  the  zenith 
distances  of  the  pairs  of  north  and  south  stars),  and  the 
differences  between  the  refractions  of  the  pairs.  The 
stars  chosen  for  this  work  are  all  fundamental,  and  in  a 
first  approximation  their  declinations  are  to  be  considered 


1 1 6  CA  LIFOKNIA  A  CA  DEMY  OF  SCIENCES.        [ PROG.  3D  SER. 

absolute.  The  list  of  stars,  given  later,  has  been  taken 
from  Professor  Newcomb's  "Catalogue  of  Fundamental 
Stars  for  1875  and  1900,  reduced  to  an  absolute  System." 
The  apparent  zenith  distances,  or  the  sums  of  the  zenith 
distances  of  the  several  pairs,  are  obtained  from  the 
Meridian  Circle  observations;  and  the  differences  in  the 
refractions  are  found  by  computing  the  refractions  from 
some  standard  table.  In  this  work  the  Pulkowa  tables 
have  been  used.  The  term  ^(rs — rn)  being  of  the  nature 
of  a  differential  refraction,  any  error  in  the  constant  of 
refraction  of  the  table  used  will  have  practically  no  effect 
upon  this  difference.  The  more  nearly  ideal  conditions 
(/.  £.,  when  rs=rn)  are  approached,  of  course,  the  better  the 
determination  of  the  refractions  will  be. 

This  method  has  both  its  advantages  and  its  disadvantages. 
Among  the  former,  the  most  important  are:  first,  the  total 
elimination  of  the  latitude  and  hence  also  of  its  variation ; 
second,  the  elimination  of  the  nadir,  since  (z's+z'n)  is 
nothing  more  nor  less  than  the  difference  between  the  circle 
readings,  and  is  therefore  independent  of  the  zenith  point; 
third,  there  is  no  wait  of  twelve  hours  or  of  six  months  in 
order  to  observe  a  star  at  both  culminations,  as  is  usually 
done;  and  fourth,  the  simplicity  of  the  reductions. 

The  greatest  disadvantage  in  this  method  lies  in  the  fact 
that  the  declinations  of  the  stars  have  to  be  considered 
known.  But  by  taking  fundamental  stars,  such  as  those 
whose  places  are  given  by  Professor  Newcomb's  new 
Fundamental  Catalogue,  and  by  taking  a  large  number  of 
these  stars,  this  difficulty  will  be  nearly  completely  eliminated. 

Having  now  the  new  refractions,  the  correction  to  the 
constant  of  the  table  used  (Pulkowa)  is  found  from  the 
following  equation  [eq.  (701)  pg.  672,  Vol.  I,  Chauvenet, 
"  Spherical  and  Practical  Astronomy'']  : 

dr=Ada  +  Bd£, 
where 

A=I 

a 

and  ,,-         ~ 

r>        -a         2    /^dQ        Q 

B  =  sm^z  +  —-  (  — -  —  — - 
\/3    W         2/3 


M.-P.— VOL.  I.]     CRAWFORD— CONSTANT  OF  REFRACTION.          117 

For  this  observatory,  whose  altitude  is  4,209  feet  and 
where  the  mean  annual  pressure  is  less  than  26  inches, 
an  investigation  into  the  effect  of  the  higher  powers  of 

A  /3  involved  in  the  factor  fi=—=  i  -) -—  =   i    -| — 

r>  B  B 

(in  Bessel's  notation  for  r)  was  necessary.  In  his  memoir, 
"  Untersuchungen  iiber  die  Constitution  der  Atmosphare 
und  die  Strahlenbrechung  in  Derselben,"  St.  Petersburg, 
1866,  (jylden  has  neglected  the  squares  and  higher  powers 

of  •%-,  since  for  places  at  low  altitudes  An  is  a  very  small 

D  '  .  D 

quantity.  This  investigation  was  made  by  Professor  Corn- 
stock  (Vol.  I,  "  Publications  of  the  Lick  Observatory"). 
From  his  investigation  the  conclusion  is  drawn  that  "  the 
Pulkowa  Refraction  Tables  may  be  used  for  atmospheric 
pressures  as  low  as  25  inches  without  taking  into  account 
the  squares  and  higher  powers  of  ^b,  and  the  quantities  so 
neglected  will  not  be  sensible  at  zenith  distances  less  than 
80°. "  The  minimum  reading  of  the  barometer  during  these 
observations  was  25.72  inches,  so  that  in  these  reductions 
no  modification  of  the  factor  of  the  refraction  depending 
upon  the  barometer  need  be  made. 

This  question  having  been  disposed  of,  the  assumption  is 
here  made  that  all  of  the  error  in  the  refractions  is  due  to 
an  error  in  the  constant  of  refraction.  This  amounts  to 
assuming  the  constant  j3  to  be  correct  or  that  d/3=o.  The 
equation  above  then  reduces  to  the  very  simple  expression 

dr  —  Ada  =  —  da ; 

hence 

da         dr 

a  r 

or  dloga  =  dlogr. 

Having  dlogr  from  the  reductions,  we  thus  have  dloga,  and 
hence  da. 

This  assumption  would  perhaps  seem  somewhat  risky  f6r 
stars  whose  zenith  distances  are  greater  than  80°.  But  at 
the  conclusion  of  the  reductions,  the  value  of  dloga  deduced 


Il8  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  3D  SER. 

from  such  stars  was  found  to  fit  in  very  well  with  those 
deduced  from  the  other  stars.  Furthermore,  down  to  85° 
zenith  distance  the  observing  was  very  good.  In  con- 
sequence of  these  facts  it  was  decided  to  take  into  account 
all  the  stars  observed.  The  zenith  distances  of  the  stars  in 
this  list  range  from  21°  21'  to  89°  12'  (apparent). 

From  85°  zenith  distance  down,  the  quality  of  the 
" seeing"  decreases  quite  rapidly.  This  can  be  seen  from 
the  following  table  of  average  weights.  These  weights 
were  derived  from  the  probable  errors  of  the  individual 
determinations  of  dloga. 

Z.  D.  Av.  Wt. 


20°  tO  30° 

2.0 

50  to  60 

7-5 

60  to  70 

7-5 

70  to  80 

ii.  8 

80  to  85 

14.8 

85  to  90 

3-6 

The  small  weight  for  the  small  zenith  distances  is  due  to 
the  fact  that  in  the  expression  for  da  the  refraction  occurs 
in  the  denominator.  The  small  weight  for  the  stars  at 
zenith  distances  greater  than  85°  is,  of  course,  due  to 
uncertainties  in  observing  at  such  low  altitudes. 

OBSERVATIONS. 

/.  List. — The  following  list  of  31  stars  was  observed  on 
seventeen  nights,  from  1899  June  7  to  1899  July  6, 
inclusive,  and  have  been  reduced  according  to  the  plan 
outlined  in  the  preceding  section.  Eleven  other  stars  were 
on  the  same  observing  list,  but  they  have  not  been  used 
here.  They  were  put  on  to  obtain  data  for  determining 
bisection  error,  and  for  other  purposes. 

The  numbers  of  the  stars  are  those  of  Newcomb's 
"  Catalogue  of  Fundamental  Stars  for  1875  and  1900, 
reduced  to  an  Absolute  System." 


M.-P.— VOL.  I.]     CRAWFORD— CONSTANT  OF  REFRACTION. 


No. 

a 

(1900) 

B  i 

1900) 

948 

14* 

Sim 

59* 

—42° 

43' 

52".  30 

190 

2 

57 

33 

+53 

6 

959 

15 

5 

6 

—  51 

43 

6  .62 

968 
977 

15 
J5 

13 

21 

29 
9 

+67 
+15 

43 
46 

35  -08 
46  -45 

984 

15 

28 

28 

—40 

49 

50  .61 

225 

3 

33 

28 

+62 

53 

33  -74 

997 

15 

39 

21 

+  6 

44 

24  -53 

1005 

15 

47 

32 

—19 

52 

5  -65 

1009 

15 

50 

+15 

59 

1  6  .46 

1019 

16 

0 

I 

+58 

49 

56  .19 

264 

4 

5 

6 

+85 

17 

29  .06 

1032 

16 

12 

21 

—49 

54 

36  -79 

282 

4 

24 

6 

+53 

37  -37 

1084 
1094 

16 
17 

52 

8 

56 
30 

+  9 
+65 

50 

49  -32 
15  -88 

1105 

17 

15 

52 

—24 

53 

59  -07 

IIIO 

17 

20 

58 

—29 

46 

35  -61 

349 

5 

26 

21 

+74 

58 

39  -95 

356 

5 

29 

54 

+85 

8 

49  .60 

U35 

17 

40 

35 

—40 

5 

17  -65 

377 

5 

46 

28 

+55 

i  .68 

1156 

17 

58 

51 

—50 

5 

53  -20 

1162 

18 

3 

48 

-45 

58 

18  .07 

406 

6 

10 

48 

+59 

2 

50  .18 

1179 

18 

19 

34 

-46 

I 

24  -50 

1182 

18 

21 

48 

—25 

28 

37  -40 

424 

6 

29 

10 

+79 

40 

22  .10 

438 

6 

45 

29 

+77 

6 

17  -47 

444 

6 

48 

37 

+58 

33 

14  .18 

1225 

19 

0 

42 

—27 

48 

59  -80 

2.  Details  of  Observations. — A  night's  program  consisted 
in  observing  the  above  list,  together  with  three  nadirs,  one 
before,  one  during,  and  one  after  the  observing  of  the  stars. 
As  has  been  pointed  out,  the  nadirs  are  not  necessary  for 
the  refraction  determinations,  but,  were  taken  for  the 
reduction  of  the  latitude,  which  is  a  problem  practically 
inseparable  from  the  main  one  undertaken  here. 

No  transits  were  observed  during  these  observations,  the 
whole  attention  being  devoted  to  the  observations  for  zenith 
distance.  The  telescope  was  set  to  the  nearest  2'  and  not 
disturbed  until  the  observation  had  been  completed.  The 
bisection  was  made  (with  but  a  very  few  exceptions)  at  the 
central  transit  wire,  by  means  of  the  declination  micrometer. 
For  the  sake  of  uniformity  every  star  was  bisected  but  once 
during  its  transit.  Because  of  unavoidable  circumstances  a 
few  of  the  stars  had  passed  the  meridian  before  the  bisection 


120 


CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 


could  have  been  made.  In  these  cases  the  readings  have 
been  reduced  to  the  meridian. 

For  the  position  of  the  circle  four  microscopes  were  read. 
Settings  were  made  upon  two  scratches  under  every  micro- 
scope. The  circle  microscopes  were  usually  read  after  the 
star  had  been  bisected.  In  a  few  cases,  because  of  a 
following  star  culminating  very  soon,  the  microscopes  were 
read  before  the  bisection.  In  such  cases  the  position  of  the 
circle  was  quickly  checked  after  the  bisection. 

The  correction  for  funs  for  a  night  was  obtained  from  all 
of  the  microscope  readings  of  the  night.  This  correction 
has  been  applied  to  all  of  the  observations.  Its  values  for 
the  several  nights  of  observing  are  given  in  the  following 
table:  — 


Date 

R 

Date 

R 

Date 

R 

June    7 

+o".o6 

June  19 

-J-0".02 

June  30 

-f  o"  .  06 

8 

-j-o  .08 

21 

+o  .03 

July    3 

H-o  .07 

9 

+o  .08 

22 

+0   -03 

4 

+o  .08 

12 

+o  .05 

27 

+o  .04 

5 

+o  .05 

13 

+o  .03 

23 

+o  .07 

6 

-fo  .08 

14 

+o  .07 

29 

+  0   .06 

These  corrections  were  applied  to  the  circle  readings  to 
reduce  them  to  the  mean  position  of  the  two  scratches;  so 
that  for  a  reading  of  o"  the  correction  is  -J-R,  for  6ov  it  is  o, 
and  for  120"  it  is  — R. 

In  the  few  cases  where  the  bisections  were  made  a  little 
late  the  reductions  to  the  meridian  were  computed  from  the 

formula, 

,       sin2  \  (r — m)  , 

S  =  8 : sin  20 

sin  i 

The  horizontal  flexure  in  this  instrument  is  very  small. 
In  his  work  published  in  Vol.  IV,  "  Publications  of  the  Lick 
Observatory,"  Astronomer  Tucker  adopts  the  correction 
o".isin  Z.-  D.,  which  was  determined  from  a  series  of 
observations  extending  over  two  and  a  half  years.  In  this 
work  but  two  observations  for  flexure  were  made,  one  on 
1899  June  3,  and  the  other,  1899  July  8.  The  mean  of 


M.-P.— VOL.  I.]     CRA  WFORD— CONSTANT  OF  REFRA CTION.          121 


the  two  gives  the  correction  — o".oisin  Z.  D.;  so  that  for 
these  observations  the  flexure  correction  has  been  considered 
zero.  The  mean  of  the  values  of  one  revolution  of  the 
declination  micrometer,  determined  at  the  same  time,  is 
48". 05.  The  value  adopted,  as  noted  before,  is  48".  10. 

For  the  computation  of  the  preliminary  refractions 
(called  r'  in  the  reductions)  the  Pulkowa  tables  have  been 
used.  The  reductions  for  the  barometer,  for  the  attached, 
and  for  the  external  thermometers  were  taken  from  Vol.  I, 
"  Publications  of  the  Lick  Observatory." 

The  graduation  errors  of  the  i°  divisions  of  the  fixed 
circle  have  been  determined  by  Aetronomer  Tucker.  His 
results  are  given  in  Vol.  IV,  "  Publications  of  the  Lick 
Observatory."  He  says  there,  in  part:  "The  probable 
error  of  a  reading  upon  four  divisions  of  the  fixed  circle 
due  to  graduation  may  be  adopted  as  ±o".i5.  *  *  "  * 
There  is  some  evidence  of  periodic  character  in  the  errors, 
and  it  may  be  assumed,  in  absence  of  further  data,  that 
the  probable  error  due  to  errors  of  graduation  is  not 
diminished  by  reading  upon  two  adjoining  divisions  under 
each  microscope.  *  *  *  The  largest  error  measured  is 
o".7  for  the  mean  of  four  divisions." 

The  errors  are  not  sufficiently  systematic  to  warrant 
interpolating  for  undetermined  divisions,  so  that  no  correc- 
tion for  division  error  has  been  applied. 

Three  nadirs  were  observed  every  night.  The  changes 
during  a  night  were  usually  very  small.  The  following 
table  gives  the  means  of  the  three  determinations  on  the 
several  nights: 


Date 

Nadir 
134°  57'. 

t 

Date 

Nadir 
134°  57' 

t 

June   7 

22".  87 

62° 

June  27 

20".  95 

66° 

8 

22  .18 

66 

28 

21  .32 

67 

9 

22  .14 

69 

29 

21  .40 

69 

12 

24  .41 

'  57 

3o 

21  .70 

66 

13 

22  .70 

62 

July  3 

21  .43 

72 

14 

21  .6l 

70 

4 

21  .46 

69 

19 

23  .81 

57 

5 

22  .91 

61 

21 

22  .36 

66 

6 

22  .10 

58 

22 

21  -59 

67 

122  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 

All  of  the  observations  were  taken  with  the  fixed  circle 
west.  Had  more  time  been  available  the  instrument  would 
have  been  reversed. 

Weights,  ranging  from  5,  the  highest,  to  I  (occasionally 
j^),  the  lowest,  were  arbitrarily  assigned  to  all  the  obser- 
vations. Judgment  on  a  weight  was  formed  from  the 
steadiness  of  the  image  during  the  observation.  These 
weights  have  been  applied  all  through  the  reductions. 

j.  Reduction  of  Observations. —  The  first  thing  done 
on  the  reductions  was  to  take  the  means  of  the  microscope 
readings  and  to  apply  the  micrometer  corrections,  giving 
the  circle  readings  (called  C'  in  the  tables  following). 
The  means  of  the  microscopes  were  checked  by  taking 
the  difference  of  every  microscope  reading  from  the  mean 
of  .the  four.  If  the  sums  of  these  differences  for  the  two 
opposite  pairs  of  microscopes  was  the  same,  the  mean  was 
correct.  The  corrections  for  the  micrometers  were  checked 
by  duplicating  this  part  of  the  work. 

From  the  readings  C7  the  quantity  B  [equations  (II)  and 
(III)]  is  obtained.  The  terms  A  and  A'  of  these  equations 
are  obtained  from  the  declinations. 

The  declinations  have  been  reduced  to  1899.0  by  means 
of  the  data  furnished  in  Newcomb's  Catalogue.  The 
reductions  to  apparent  places  were  computed  by  using  the 
Besselian  Star  Numbers  from  the  American  Ephemeris. 
The  factors  a',  b',  c'  and  d'  were  computed  from  the 
American  Ephemeris  data.  The  reductions  to  apparent 
places  for  the  first  night  (June  7)  were  computed  by  means 
of  the  Independent  Star  Numbers  also.  The  places  for 
the  remaining  nights  were  checked  by  differences.  The 
apparent  declinations  are  placed  in  the  columns  S  of  the 
tables  given  later. 

The  following  table  exhibits  the  stars'  approximate  zenith 
distances  and  the  stars  with  which  they  are  grouped  in  the 
reductions  for  the  refractions : 


M.-P.— VOL.  I.]     CRAWFORD— CONSTANT  OF  REFRACTION. 


I23 


STAR  No. 

Z.  D. 

SOUTH 

Z.  D.  NORTH 

GROUPED  WITH 
STAR  No. 

948 

0 

79 

59-9 

0  .         / 

225  /.  c. 

190  /.  c.  • 

89    12.0 

959 

959 

88 

45-5 

{  282/1^. 

968 

30    22.9 

997 

977 

21 

33-2 

1019 

984 

78 

6.6 

225  /.  c. 

948 

225  /.  c. 

79   41-9 

•  984 

1135 

997 

30 

35-5 

968 

1005 

57 

"•3 

f  264  /.  c. 

1009 

21 

20.7 

1019 

1019 

21   29.3 

f  977 
\  1009 

264  /.  c. 

57   21.0 

1005 

1032 

87 

3-1 

377  /•  c. 

282  /.  c. 

88   40.0 

959 

1084 

27 

48.1 

1094 

1094 

28   29.4 

1084 

1105 

62 

12.9 

424  /.  c. 

IIIO 

67 

349  /.  c. 

349  /•  c. 

67   39.0 

IIIO 

356  /.  c. 

57   29.5 

1005 

H35 

77 

22.1 

225  /.  c. 

377  /.  c. 

86   47-2 

f  1032 

11156 

1156 

87 

13-9 

377  /.  c. 

1162 

83 

12.4 

[  406  /.  c. 

\  444  /.  c. 

406  /.  c. 

83   30-2 

f  1162 

\ii79 

1179 

83 

15-5 

/  406  /.  c. 
\  444  I.e. 

1182 

62 

47-5 

424  /.  c. 

424  /.  c. 

62   57-5 

{1105 

\Il82 

438  /.  c. 

65   31-4 

1225 

444  /.  c. 

83   59-3 

/  Il62 

1  1179 

1225 

65 

7-7 

438  /.  c. 

It  will  be  noticed  from  this  table  that  some  of  the  stars 
are  grouped  with  two  others  and  that  one  is  grouped  with 
three  others. 

(  3  >  May  6,  1903. 


124  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 

The  following  tables  show  the  reductions  for  the  new 
refractions.  The  column  ^  contains  the  means  of  the 
weights  of  the  pairs  of  stars.  The  other  columns  have 
already  been  explained.  In  the  grouping  of  the  pairs  on 
the  several  dates  the  northern  star  is  written  first  and  the 
southern  star  below  it.  The  numbers  of  the  stars  given  at 
the  tops  are  arranged  in  this  same  order.  The  pairs  which 
have  their  northern  stars  at  upper  culmination  are  placed 
first.  It  will  be  noticed  that  the  headings  of  the  columns 
for  these  pairs  are  slightly  different  from  the  later  ones 
containing  the  lower  culmination  stars. 

Because  of  very  bad  "seeing"  or  of  occasional  accidents, 
some  of  the  stars  were  not  observed  on  some  nights.  In 
such  cases  blanks  appear  after  the  dates.  No  observations 
have  been  rejected. 


M . -P.  —VOL.  I .  ]     CRA  WFORD—  CONS TA  NT  OF  REFRA  CTION.          125 


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M.-P.-VOL.  I.]      CRAW  FORD- CONSTANT  OF  REFRACTION.          167 


The  following  tables  contain  the  reductions  for  dlogr  or 
its  equivalent  dloga.  The  second  column  contains  the 
logarithms  of  the  computed  refractions;  the  next  column 
contains  the  logarithms  of  the  observed  refractions;  the 
fourth  the  difference  between  the  two  preceding,  in  the 
sense  of  Observed — Computed;  the  column^  contains  the 
weights  and  the  last  column  the  weighted  differences. 
The  residuals  and  their  weighted  squares  are  not  given. 
Log  \_-pw~\  is  given  in  every  case,  as  is  also  the  resulting 
probable  error  of  the  weighted  mean  of  every  set.  All  of 
the  results  in  the  following  tables  have  been  checked. 

STAR  No.  948. 


Date 

log.  r  ' 

log.  r 

A 

/ 

/A 

June  7 

2.42742 

2.42617 

—  0.00125 

4 

—  0.00500 

8 

2.42399 

2.42119 

280 

4 

—     1  120 

9 

2.42126 

2.41762 

364 

3 

—     1092 

12      2.43095 

2.42727 

368 

i 

368 

13 

2.42658 

2.42490 

1  68 

2 

336 

14 

2.42169 

2.41838 

33i 

3 

993 

19 

2.43214 

2.42889 

325 

3 

975 

21 

2.42478 

2.42185 

293 

4 

—    1172 

22 

2.42149 

2  .  42042 

107 

3^ 

375 

27 

2.42459 

2.42243 

—    216 

5 

—    1080 

28 

2.42313 

2.42147 

166 

2^ 

4i5 

29 

2.42262 

2.42014 

248 

3^ 

868 

3° 

J"iy  3 

2.41600 

2.41678 

+     78 

2^ 

+    195 

4 

2.41916 

2.4l8l6 

IOO 

5 

500 

5 

2  .  42644 

2  .  42605 

39 

3 

117 

6 

2.43042 

2.42602 

—    440 

l# 

—    660 

I     —  0.00205 


[p]  =  50^  ;  logpw\  =  5-8653 


p.  e.  =  ±  0.00015 


1  68 


CALIFORNIA  ACADEMY  OF  SCIENCES.       [PROC.  3D  SER. 


STAR  No.  190  /.  c. 


Date 

log.  r  ' 

log.  r 

A 

P 

/A 

June    7 

9 

3.09609 

3.08699 

—  0.00910 

3 

—  0.02730 

12 

3.10852 

3-09598 

—       1254 

i 

—       1254 

13 

3.10231 

3  .  10302 

+          71 

% 

+            35 

H 

3.09619 

3.09129 

490 

3 

—        1470 

19 

21 

3.10009 

3-09349 

—        660 

4 

—        2640 

22 

3-09543 

3-09387 

156 

^ 

546 

27 

3-09851 

3.09629 

—              222 

5 

—        mo 

28 

3-09793 

3.09046 

747 

3 

2241 

29 

3.09748 

3.08610 

-        1138 

3 

—        34M 

30 

3.09728 

3-09563 

165 

4 

660 

July     3 

4 

3.09289 

3.08925 

364 

5 

—         1820 

I 

3.10261 

3-097I3 

548 

3 

—        1644 

::=  38; 


=  6.6II2 


A  —  0.00513 


p.  e.  = 


0.00047 


STAR  No.  959.— (With  190 /.  c.) 


Date 

/£>£•.  r  ' 

log.  r 

A 

P 

/A 

June    7 

O 

9 

3-03783 

3.02741 

—  0.01042 

3 

—  0.03126 

12 

3.05008 

3-0357I 

—       H37 

i 

—      1437 

13 

3-04374 

3-04454 

+          80 

/^ 

+       40 

14 

3-037I4 

3-03I75 

539 

3 

—        1617 

21 

3.04205 

3-0345I 

754 

4 

3016 

22 

3.03782 

3-03605 

177 

619 

27 

3.04138 

3-03886                        252 

5 

—         1260 

28 

3.04032 

3-03I77                        855 

3 

—      2565 

29 

3-03986 

3.02685           —        1301 

3 

—      3903 

3° 

3-03983 

3-03795 

—          188 

4 

—       752 

July     3 

4 

3  .  03667 

3-03252 

—          415 

5 

—      2075 

5 

3.04442 

3-03815 

627 

3 

—        1881 

6 

A     I 


o . 00584 


[p  ]  =  38  ;  log 


=  6.  7298 


P-e.=±  0.00053 


M.-P.— VOL.  I.  ]     CRA  WFORD—  CONST  A  NT  OF  REFRA  CTION.          1 69 
STAR  No.  959. -(With  282  /.  c.) 


Date 

, 

log.  r 

A 

P 

/A 

June  7 

3.04492 

3  .  04068 

—  0.00424 

M 

—  0.01908 

8 

3.04160 

3.03886 

274 

3^2 

959 

9 

3-03783 

3-03050 

733 

3 

-    2199 

12 

3  .  05008 

3-04703 

3°5 

i 

—    305 

13 

3-037I4 

3-03633 

—     81 

3 

243 

19 

3-05165 

3.04787 

378- 

3 

21 

3.04205 

3-03741 

464 

4 

—    1856 

22 

3.03782 

3-03645 

137 

3/^ 

479 

27 

3.04138 

3-037I7 

421 

5 

—   2105 

28 

3.04032 

3.03228 

804 

2/^ 

—     2OIO 

29 

3.03986 

3-03043 

943 

3t 

—     2829 

3° 

3-03983 

3.03611 

—    372 

—     1674 

July  3 

4 

3.03667 

3.03112 

555 

5 

—     2775 

5 

3.04442 

3.03910 

532 

3/^ 

—     1862 

6 

3.04920 

3-04347 

—    573 

2/^ 

1432 

|      —  0.00462 


=  5i#  J  log[pvv]  =  6.3662 


p.  e.  =  ±  0.00027 


STAR  No.  968. 


Date 

/qg\  r  ' 

log.r 

A 

P 

/A 

June  7 

1.45651 

.46180 

+  0.00529 

4 

-f-  0.02116 

8 

.45383 

•46553 

+   1170 

4 

4680 

9 

I.45H9 

•45637 

488 

3 

1464 

12 

.45985 

.46790 

805 

i 

805 

13 

•456i4 

•46225 

611 

I# 

916 

M 

.45172 

.45758 

586 

3 

1758 

19 

.  46276 

•46879 

603 

3 

1809 

21 

-45485 

.46374 

889 

3K 

3111 

22 

.45181 

.46120 

939 

3^ 

3286 

27 

•45453 

•45652 

199 

5 

995 

28 

.45407 

.46060 

653 

2^ 

+    1632 

29 

•45340 

•45984 

644 

3^ 

2254 

3° 

July  2 

•44653 

•45347 

+    694 

3 

-f    2082 

4 

.45114 

.45408 

294 

5 

1470 

5 

•45656 

1.46835 

1179 

3 

3537 

6 

.46066 

1.46850 

+    784 

ig 

+    1176 

0.00662 


[P  }  =  5°  ; 


=  6.  6307 


p.  e.  =  ±  0.00036 


1 70  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 

STAR  No.  977. 


Date 

**;< 

log.  r 

A 

* 

/A 

June  7 

i  .  28488 

.  28488 

^  o.ooooo 

4 

^  o.ooooo 

8 

1.28218 

.  28892 

-f-    674 

4 

+   2696 

9 

.28019 

.28126 

107 

3 

321 

12 

.28796 

.  29270 

474 

i 

474 

13 

.  28439 

.29491 

+    1052 

1^2 

1578 

.  28022 

.29092 

1070 

3 

3210 

19 

.29163 

173 

3£ 

519 

21 

.28336 

.28758 

422 

H77 

22 

.  28043 

.28149 

106 

3/^ 

37i 

27 

.  28302 

.28758 

456 

5 

2280 

28 

.  28288 

•28533 

245 

612 

29 

.  28206 

.28691 

485 

3^2 

1697 

30 

.  28204 

.  28648 

444 

4 

+    1776 

July  3 

.27518 

.28171 

653 

3 

1959 

4 

i  .28003 

.28758 

755 

5 

3775 

5 

1.28512 

•  29623 

mi 

3 

+    3333 

6 

i  .  28948 

.  28870 

-     78 

2 

156 

I      +  0.00476 


=  541A  ;  log  [pvv}  =  6.7951 


STAR  No.  984. 


p.  e.  = 


0.00040 


Date 

/0g\  r  ' 

log.r 

A 

/ 

/A 

June    7 

9 

- 

12 

2  .  35626 

2-35I99           —  0.00427 

I 

—  0.00427 

J3 

2.35336 

2.35114                                   222 

2^ 

555 

14 

2.34902 

2.34616                      286 

3 

858 

19 

2.36071 

2.35971 

IOO 

3 

300 

21 

2.35175 

2.35042                  133 

3 

399 

22 

2-34937 

2.34805                132 

3^ 

462 

27 

2.35175 

2.34951                  224 

5 

1  1  20 

28 

2.35162 

2.35176        +         14 

2 

+                  28 

29 

2  .  35060 

2.34874           —          i  86 

4 

744 

3° 

July    3 

2.34417 

2.34616 

•f       199 

3 

+          597 

4 

2  •  34844 

2.34713 

131 

5 

655 

5 

2.35414 

2.35319                          95 

3 

-          285 

6     1      2.35871 

2.35581                        290 

i# 

—          435 

A 

—  0.00142 

[pvv]  =  5.8091 


p.  e.  =  ^E  0.00017 


M.-P.— VOL.  I.] -7  CRA  WFORD—  CONSTANT  OF  REFRA CTION.          171 
STAR  No.  225  /.  ^r.— (With  948.) 


Date 

%"•  f  ' 

log.  r 

A 

/ 

/A 

June    7 

2-41352 

2.41224 

—  0.00128 

4 

—  0.00512 

8 

2.41100 

2.40812 

288 

4 

—       1152 

9 

2.40895 

2.40523 

372 

3 

—        1116 

12 

2.41618 

2.41237 

381 

i 

38i 

13 

2.41359 

2.41187 

172 

2 

344 

H 

2.40930 

2  .  40591 

339 

3 

—        1017 

19 

2.42102 

2.41769 

333 

3 

999 

21 

2.41181 

2  .  40880 

301 

4 

—         1204 

22 

2.40967 

2.40858 

109 

3^ 

38i 

27 

2.41188 

2  .  40966 

222 

5 

—            IIIO 

28 

2.4H75 

2.41007 

168 

2^ 

420 

29 

2.41072 

2.40815 

257 

3^ 

899 

3° 

July    3 

2.40463 

2.40542 

+            79 

2^ 

+           197 

4 

2.40845 

2.40741 

104 

5 

—          520 

5 

2.41441 

2.41400 

4i 

3 

123 

6 

2.41907 

2.41457 

—          45o 

I# 

-          675 

—    0.002II 


[/ 1  =  50^  ;  log  [pvv ]  =  5.8809 


STAR  No.  225  /.  c.— (With  984.) 


p.  e.  = 


0.00015 


Date 

•r.r- 

log.r 

A 

> 

/A 

June    7 

8 

9 

12 

2.41618 

2.41246 

—  0.00372 

i 

—  0.00372 

13 

2.41359 

2.41165 

194 

2% 

485 

2.40930 

2  .  40678 

252 

3 

756 

19 

2.42102 

2.42014 

—            88 

3 

264 

21 

2.41181 

2.4IO66 

115 

3 

345 

22 

2.40967 

2  .  40849 

.  —          118 

413 

27 

2.41188 

2.40983 

205 

5 

—        1025 

28 

2.41175 

2.41186 

+            ii 

2 

+                 22 

29 

2.41072 

2.40914 

158 

4 

632 

3° 

July    3 

4 

2  .  40463 
2.40845 

2.40637 
2.40729 

4-        i74 

116 

3 
5 

+              522 

580 

5 

2.4I44I 

2.41357 

84 

3 

—              252 

6 

2.41907 

2.41652 

—          255 

382 

|      —  0.00126 


[p  ]  =  39^  ;  log  [pvv  1  =  5-6934 


p.  e.  = 


0.00015 


(6) 


May  9,  1903. 


172  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  3D  SER. 

STAR  No.  225  /.  c.— (With  1135.) 


Date 

log.  r  ' 

log.  r 

A 

P 

/A 

June  7 

2.41352 

2.41299 

—  0.00053 

4^ 

—  0.00238 

8 

2.41100 

2  .  40928 

172 

4 

688 

9 

2.40895 

2.40601 

294 

3 

882 

12 

2.41618 

2.41416 

202 

i 

202 

J3 

2.41359 

2.4II05 

254 

2 

508 

14 

2.40930 

2.40724 

—      2O6 

3 

618 

19 

2.42102 

2.41858 

244 

3 

732 

21 

2.41181 

2.4IIOO 

81 

4 

324 

22 

2.40967 

2  .  40882 

85 

4 

340 

27 

2.41188 

2.40981 

—    207 

5 

—    1035 

28 

2.41175 

2.4IIOO 

2^ 

187 

29 

2.41072 

2.40744 

328 

4 

—    1312 

3° 

July  3 

2.40463 

2.40488 

+     25 

3 

+     75 

4 

2.40845 

2.40691 

154 

5 

770 

5 

2.41441 

2.41437 

4 

3^ 

—     14 

6 

2.41907 

2.41547 

360 

2 

—    720 

=  5.7856 


A     I 


0.00159 


P>  e>  — 


0.00013 


STAR  No.  997. 


Date 

/cjg-.  r  ' 

log.r 

A 

/ 

/A 

June    7 

1.45932 

1.46479 

+  0.00547 

4 

-f-  0.02188 

8 

I.45705 

1.46879 

1174 

4 

4696 

9 

1.45504 

1.45969 

465 

3 

+       1395 

12 

1.46180 

1.46967 

787 

i 

787 

13 

1-45953 

I-46553 

600 

i# 

900 

14 

1-45544 

i  .46120 

576 

3 

1728 

19 

i  .  46676 

1.47261 

585 

3 

1755 

21 

•45774 

i  .  46642 

868 

3^ 

3038 

22 

•45588 

1.46509 

921 

3^ 

3223 

27 

•45791 

1.45984 

193 

5 

965 

28 

•45782 

1.46419 

637 

2^ 

+       1592 

29 

•45671 

1-46315 

644 

3^ 

+       2254 

3° 

July    3 

1.45099 

1-45773 

-f          674 

3 

-|-            2O22 

4 

I.45436 

1.45712 

+        '276 

5 

I380 

5 

i  .  46049 

1.47217 

1168 

3 

3504 

6 

i  .  46492 

1.47261 

+          769 

i# 

+            U53 

[p  ]  =  50  ;  log  \_pvv]  =  6.6325 


A     I      +  0.00652 
p.  e.  =  Jz  0.00036 


M.-P.— VOL.  I.]     CRAWFORD— CONSTANT  OF  REFRACTION.          173 
STAR  No.  1005.— (With  264  /.  c.) 


Date 

/<£•.  r  ' 

log.r 

A 

P 

/A 

June  7 

.87711 

1.87518 

—  0.00193 

4 

—  0.00772 

8 

.87496 

1.87186 

310 

4 

—   1240 

9 

.87269 

.86700 

569 

3 

—   1707 

12 

.87989 

.87697 

292 

i 

292 

13 

.87719 

.87361 

358 

2 

716 

H 

.87307 

•87454 

+    H7 

3 

+   44i 

19 

•88455 

.88138 

3!7 

3 

95i 

21 
22 

.87581 
.87378 

:  86964 

348 
414 

4 

4 

-   1392 
—   1656 

27 

-87582 

.87489 

93 

5 

465 

28 

•87565 

.87093 

472 

2 

944 

29 

.87436 

.87256 

180 

4 

720 

30 

.87545 

.87489 

56 

4 

224 

July  3 

.86915 

.86847 

68 

3 

204 

4 

.87220 

.87157 

63 

5 

3*5 

5 

1.87863 

.87823 

40 

3 

1  20 

6 

1.88269 

.87881 

-    388 

2 

-    776 

=  56  ;  log 


=  6.2452 


A     I      —  0.00215 

P.  e.  ••= 


STAR  No.  1005.— (With  356  /.  c.) 


Date 

log.  r  ' 

log.  r 

A 

P 

/A 

June  7 

9 

.87269 

•87233 

—  0.00036 

3 

—  0.00108 

12 

.87989 

.87800 

189 

i 

189 

13 

.87719 

•87547 

172 

2^ 

43° 

14 

.87307 

•87355 

+    48 

3 

144 

19 

-88455 

.88502 

+     47 

3 

+    HI 

21 

.87581 

•87413 

168 

4 

672 

22 

.87378 

.87268 

no 

4 

44o 

27 

-87582 

.87743 

-f    161 

5 

+    805 

28 

•87565 

•87425 

140 

2 

—    280 

29 
30 

.87436 
•87545 

.87512 
.87714 

+     76 
+    169 

4 
4 

+    304 
+    676 

July  3 

•86915 

.86788 

127 

3 

381 

4 

.87220 

.87326 

+    106 

5 

+    53° 

5 

.87863 

.87547 

3i6 

3^ 

—    1106 

6 

.88269 

.88064 

—    205 

2^ 

—    512 

A     I     —  0.00031 


[P  ]  =  49 %  ;  log  [pvv]  =  6.0442 


p,  e.  = 


0.00019 


174  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  3D  SER. 

STAR  No.  1009. 


Date 

&#•.  r  ' 

log.r 

A 

P 

/A 

June  7 

.27967 

.27600 

—  0.00367 

4 

—  0.01468 

9 

•27759 
•27515 

.  28149 
.28149 

390 
+   634 

4 
3 

+   1560 
4-   1902 

12 

.  28250 

.  28240 

—       10 

IO 

13 

.27963 

•  28307 

+    344 

2 

+    688 

14 

•  27547 

.  28262 

7i5 

3 

2H5 

J9 

.  28706 

.28825 

119 

3 

357 

21 

•  27843 

•  27989 

+    146 

4 

22 

.  27648 

•  27346 

302 

4 

—    1208 

27 

•  27834 

.28511 

+    677 

5 

+    3385 

28 

.27819 

1.28126 

307 

2 

614 

29 

.  27674 

1.28149 

475 

4 

1900 

30 

.27815 

1-28375 

560 

4 

2240 

July  3 

4 

.27187 
•27473 

1.27300 
1.27807 

U3 

334 

3 

5 

339 
1670 

5 

1.28132 

i  .  28466 

334 

3 

1  002 

6 

1.28519 

1.29003 

+    484 

2 

+    968 

=  56  ;  log  [pvv]  =  6.7629 


I      +  0.00298 


p.  e.  =  zt  0.00038 


Star  No.  1019— (With~977.) 


Date 

log.  r  ' 

log.r 

A 

P 

/A 

June  7 

.28286 

.  28307 

+  0.00021 

4 

-(-  0.00084 

8 

•28075 

.28758 

683 

4 

2732 

9 

.27851 

.  27987 

136 

3 

408 

12 

.28578 

.  29048 

470 

i 

470 

13 

.28283 

•  29358 

1075 

I* 

1612 

H 

.27867 

•  28959 

1092 

3 

3276 

19 

-  29036 

.  29203 

I67 

3 

501 

21 

.28165 

.  28623 

458 

3^ 

1603 

22 

.  27970 

.28103 

133 

3^ 

465 

27 

.28158 

.  28623 

465 

5 

2325 

28 

.28158 

.28398 

240 

2^ 

600 

29 

.  27989 

.  28466 

477 

3^ 

1669 

30 

.28139 

.  28601 

462 

4 

1848 

July  3 

•  27536 

.28171 

635 

3 

1905 

4 

•  27798 

•28578 

780 

5 

3900 

5 

.  28468 

•  29579 

-j-    mi 

3 

+   3333 

6 

.28837 

.  28780 

—     57 

2 

—    114 

=.  54 /^  i  log[pw]  =  6.7903 


A     I     +  0.00488 


.  e.  =  ±  0.00040 


M.-P.— VOL.  I.]     CRA  WFORD- CONSTA NT  OF  REFRA  CTION.          175 
STAR  No.  1019 -(With  1009.) 


Date 

/0£-.  r  ' 

log.  r 

A 

P 

/A 

June  7 

.  28286 

.27921 

—  0.00365 

4 

—  0.01460 

8 

.  28075 

.  28466 

391 

4 

+   1564 

9 

.27851 

.  28466 

+   615 

3 

+   1845 

12 

.28578 

.28556 

22 

i 

22 

13 

.28283 

.28623 

340 

2 

-f      680 

H 

.27867 

.28578 

711 

3 

2133 

19 

.  29036 

.29137 

101 

3 

303 

21 

.28165 

.28307 

142 

4 

+      568 

22 

.  27970 

.27669 

301 

4 

—     1204 

27 

.28158 

.28825 

+      667 

5 

+    3335 

28 

.28158 

.28443 

285 

2 

57o 

29 

•  27989 

.28466 

477 

4 

1908 

3° 

.28139 

.28691 

552 

4 

-j-    2208 

July  3 

•  27536 

•  27623 

87 

3 

261 

4 

.  27798 

.28126 

328 

5 

1640 

5 

.  28468 

.  28780 

312 

3 

936 

6 

•  28837 

.293H 

+    477 

2 

+    954 

A 

-f-  0.00290 

\.p}  =  56 ;  log  [pvv ]  =  6.7654 


STAR  No.  264  /.  c. 


P-  £•  =  it  0.00038 


Date 

log.  r  ' 

log.  r 

A 

P 

/A 

June  7 

.87981 

•87783 

—  '0.00198 

4 

—  0.00792 

8 

.87779 

.87466 

313 

4 

—   1252 

9 

.87564 

.86994 

570 

3 

—   1710 

12 

.88285 

.87996 

289 

i 

289 

J3 

.87988 

.87628 

360 

2 

720 

H 

.87560 

.87697 

+    137 

3 

+    411 

19 

.88743 

.88423 

320 

3 

960 

21 

.87852 

.87500 

352 

4 

—   1408 

22 

•87657 

•87245 

412 

4 

—   1648 

27 

•87853 

.87754 

99 

5 

495 

28 

.87878 

.  87408 

470 

2 

940 

29 

•87673 

.87489 

184 

4 

736 

30 

.87825 

1.87766 

59 

4 

236 

July  3 

.87237 

•87163 

74 

3 

—      222 

4 

•  87492 

.87425 

67 

5 

335 

5 

.88164 

1.88121 

43 

3 

129 

6 

.88517 

1.88133 

-    384 

2 

-    768 

A 


—  0.00218 


[p  ]  =  56  ;  log  [pw}  =  6. 2338 


p.  e.  =  -r  0.00020 


176  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 

STAR  No.  1032. 


Date 

log.  r  ' 

log.  r 

A 

P 

/A 

June  7 

8 

9 

12 

13 

2  .  85820 

2.86091 

-f  0.00271 

i 

-j-  0.00271 

14 

2  .  85280 

2.85044 

236 

3^ 

826 

*9 

2.86657 

2.86178 

479 

3 

—   1437 

21 

2-85637 

2.85442 

195 

4 

780 

22 

2.854II 

2.85258 

—    153 

4 

612 

2 

2  .  85620 
2.85690 

2.85429 
2.85286 

191 

404 

\x 

955 

—     IOIO 

29 

2.85421 

2.84821 

—    600 

3^ 

2IOO 

3° 

2.85600 

2.84956 

644 

4 

—     2576 

July  3 

2.84957 

2.84596 

36i 

3 

—     I083 

4 

2.85239 

2.85174 

65 

4^ 

292 

5 

2.86022 

2.85728 

294 

4 

—     1176 

6 

2.86417 

2.85807 

—    610 

2j^ 

—     1525 

|     —  0.00317 


[p]  =  44%  ;  log  [pvv]  =  6.2854 


STAR  No.  282  /.  c. 


p.  e.  = 


0.00029 


Date 

%.r' 

log.r 

A 

P 

PA 

June    7 

3-03250 

3.02825 

—  0.00425 

4^ 

—   O.OI9I2 

8 

3.02963 

3.02682 

281 

3# 

983 

9 

3  .  02804 

3-02054 

750 

3 

—           2250 

12 

3.03690 

3.03376 

314 

i 

3H 

13 

14 

3.02661 

3-02556 

105 

3 

315 

19 

3.04241 

3-03855 

386 

3 

—            H58 

21 

3-03063 

3.02586 

477 

4 

—            1908 

22 

3.02814 

3.02674 

140 

3/^ 

490 

27 

3.03018 

3.02586 

432 

5 

—            2l6o 

28 

3.03140 

3.02319 

—          821 

2/^ 

—            2052 

29 

3.02815 

3.01847 

968 

3x 

—           2904 

30 

3.02989 

3  .  02608 

381 

—            1714 

July    3 

4 

3.02636 

3  .  02069 

567 

5 

-            2835 

5 

3-035II 

3.02968 

543 

3/^ 

—            I9OO 

6 

3.03907 

3.03320 

587 

2^ 

—            1467 

A     |     —  0.00473 


log  [pvv]  =  6.3770 


p.  e.  — 


0.00027 


M.-P.—  VOL.  I.]     CRAWFORD—  CONSTANT  OF  REFRACJ^ION.          177 
STAR  No.  1084. 


Date 

log.  r  ' 

log.  r 

A 

p 

/A 

June  7 

I-40959. 

1.41263 

-\-  0.00304 

5 

-f-  0.01520 

8 

.40788 

1.40157 

63i 

4 

—   2524 

9 

.40678 

.40790 

+      H2 

3 

+    336 

12 

•41235 

.41162 

73 

i 

13 

.41026 

.41145 

+    119 

2 

+    238 

14 

•40551 

.40381 

170 

3 

510 

19 

.41774 

.41681 

93 

3 

279 

21 

.40831 

.40976 

-f    J45 

4 

+   1256 

22 

.40704 

.40432 

^272 

4 

—   1088 

27 

.40883 

.  40926 

+  :  43 

5 

+    215 

28 

.40783 

.  40892 

'  109 

2 

218 

29 

.40587 

.40500 

-  I  '87 

3 

261 

3° 

.  40780 

.41010 

'  230 

4 

+    920 

July  3 

.40181 

•39863 

318 

3 

954 

4 

•40565 

•40552 

13 

5 

65 

5 

•4II59 

.40449 

710 

4 

2840 

6 

.41433 

•40993 

—   440 

3 

—    1320 

A      I      —  o.ooioi 


[/]  =  58;  log[pw]  =6.7152 


STAR  No.  1094. 


p.  e.  = 


0.00035 


Date 

log.  r  ' 

log.  r 

A 

P 

/A 

June  7 

i  .  42207 

i  .  42488 

+  0.00281 

5 

-f  0.01405 

8 

.  42036 

1.41414 

622 

4 

—   2488 

9 

•41943 

.  42062 

+    119 

3 

+    357 

12 

.  42492 

.42423 

69 

i 

69 

13 

.42275 

•42374 

+     99 

2 

+    198 

14 

.41809 

.41631 

178 

3 

534 

19 

.43008 

.42894 

114 

3 

342 

21 

.  42082 

.42210 

+     128 

4 

,  +    5i2 

22 

.41979 

.41714 

265 

4 

—   1060 

27 

•42185 

.42226 

+     4i 

5 

205 

28 

•41995 

.42095 

+      100 

2 

+      200 

29 

.41807 

.41714 

93 

3 

279 

30 

•42033 

•42243 

210 

4 

+      840. 

July  3 

.41401 

•41095 

306 

3 

9l8 

4 

.41844 

.41830 

14 

5 

70 

5 

.42416 

•4i73i 

685 

4 

—     2740 

6 

1.42679 

•42259 

—      420 

3 

I26O 

A     I 


0.00104 


p.  e.  —  ±  0.00034 


178  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  3D  SER. 

STAR  No.  1105. 


Date 

/<#-.  r  ' 

log.  r 

A 

P 

PL 

June  7 

o 

9 

1.96122 

1.95861 

-  0.00261 

3/2 

—  0.00913 

12 

T3 

.96464 

.96209 

255 

2 

510 

14 

.96010 

.96468 

+    458 

3^ 

+   1603 

!9 

.97190 

•97257 

+    67 

3 

4-      201 

21 

-96285 

•96i37 

148 

4 

592 

22 

•96i73 

.96114 

59 

4 

236 

27 

.96404 

.96161 

243 

5 

—   1215 

28 

.96169 

.96223 

+     54 

3 

+   162 

29 

•9599° 

.95985 

5 

3 

15 

3° 

.96218 

.96142 

76 

4^ 

342 

July  3 

•95599 

1-95650 

+     5i 

3 

153 

4 

.96028 

.96099 

+     7i 

5 

+    355 

5 

.96610 

1.96577 

33 

4 

132 

6 

.96874 

.96876 

+        2 

3 

+      6 

=6.1881 


A 


0.00029 


p.  e.  —  ±  0.00023 


STAR  No.  mo. 


Date 

/<?£•.  r  ' 

log.  r 

A 

P 

/A 

June    7 

2.05864 

2.05998 

+  0.00134 

5 

-f-  0.00670 

8 

2.05683 

2.05790 

+        107 

4 

+      428 

9 

2.05574 

2  .  05342 

232 

3 

696 

12 

2.06194 

2.O6OI7 

177 

i 

177 

13 

2.05916 

2.05888 

—          28 

i 

28 

14 

2.05485 

2.05778 

+        293 

3 

+      879 

19 

2  .  06659 

2  .  06446 

213 

3 

639 

21 

2.05744 

2.05637 

107 

4 

428 

22 

2.05644 

2.05319 

325 

4 

—         1300 

27 

2  .  05892 

2-05775 

117 

5 

585 

28 

2.O5622 

2-05599 

23 

2 

46 

29 

2.05450 

2.05385 

65 

4 

260 

30 

2.05679 

2.05427 

—        252 

4^ 

—      1134 

July    3 

2  .  05066 

2.04895 

171 

2^ 

427 

4 

2.05488 

2  .  05484 

4 

5 

—                 20 

5 

2  .  06079 

2  •  05964 

H5 

4 

460 

6 

2.06344 

2.o6lI9 

—          225 

3 

-      675 

I     —  0.00084 


=  58  ;  log 


=  6.1535 


p.  e.  = 


0.00018 


M.-P.— VOL.  I.]      CRAWFORD— CONSTANT  OF  REFRACTION.         179 
STAR  No.  349  /.  c. 


Date 

/<?f  .  r  ' 

log.  r 

A 

/ 

/A 

June  7 

2.07053 

2.07177 

-f-  0.00124 

5 

-f-  0.00620 

8 

2.06871 

2.06974 

4-   103 

4 

412 

9 

2.06761 

2.06539 

222 

3 

666 

12 

2.07385 

2.07210 

175 

i 

175 

13 

2.07104 

2  .  07078 

—       26 

i 

—     26 

14 

2  .  06690 

2.06971 

-f      28l 

3 

+    843 

19 

2  .  07824 

2.07613 

211 

3 

633 

21 

2  .  06933 

2.06826 

107 

4 

428 

22 

2  .  06834 

2.06517 

317 

4 

1268 

27 

2.07091 

2.06974 

117 

5 

585 

28 

2.06804 

2.06781 

23 

2 

46 

29 

2  .  06647 

2  .  06580 

67 

4 

268 

30 

2  .  06870 

2.06622 

248 

4>£ 

—   1116 

July  3 

2.06268 

2.06104 

164 

2^ 

410 

4 

2.06687 

2.06685 

—        2 

5 

10 

5 

2.07272 

2.07159 

H3 

4 

452 

6 

2-07535 

2.07316 

—      219 

3 

-    657 

A     I 


0.00084 


[p]  =  58;  log  [pvv]  =  6.1255 


STAR  No.  356  /.  c. 


p.  e.  = 


0.00018 


Date 

/0£\  r  ' 

log.  r 

A 

/ 

/A 

June  7 

o 

9 

.87922 

1.87881 

—  0.00041 

3 

—  0.00123 

12 

.88536 

.88349 

187 

i 

187 

13 

.88248 

.88076 

172 

2^ 

430 

H 

.87854 

.87898 

44 

3 

+    132 

19 

.88965 

.89009 

44 

3 

+    132 

21 

.88077 

.87910 

167 

4 

668 

22 

.87968 

.87858 

no 

4 

440 

27 

.88234 

•88395 

-|-    161 

5 

+    805 

28 

.87948 

.87806 

142 

2 

284 

29 

.87811 

.87881 

+     70 

4 

4-    280 

30 

.88005 

.88173 

+    168 

4 

+    672 

July  3 

.87414 

.87280 

134 

3 

402 

4 

.87840 

•87938 

+     98 

5 

+    49° 

5 

.88413 

.88098 

315 

3^ 

—     IIO2 

6 

.88677 

.88474 

203 

2^ 

—      507 

I     —  0-00033 


\.P  ]  = 


log  [pvv  ]  =  6.0359 


p.  e.  =  ±  0.00019 


l8o  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 

STAR  No.  1135. 


Date 

/eg-,  r  ' 

log.  r 

A 

P 

/A 

June*  7 

2.32700 

2.32638 

—  0.00062 

4K 

—  0.00279 

8 

2.32535 

2.32327 

208 

4 

832 

9 

2.32443 

2.32087 

356 

3 

—   1068 

12 

2  .  33060 

2.32816 

244 

i 

244 

13 

2.32766 

2.32457 

309 

2 

618 

14 

2  .  32400 

2.32149 

251 

3 

753 

19 

2.33465 

2.33169 

296 

3 

888 

21 

2.32578 

2.32479 

99 

4 

396 

22 

2.32463 

2.32362 

101 

4 

404 

27 

2.32747 

2.32496 

251 

5 

—    1255 

28 

2.32461 

2.32368 

93 

2^ 

—    232 

29 

2.32347 

2.31946 

401 

4 

—    1604 

30 

July  3 

2.31931 

2.31962 

+     3i 

3 

+     93 

4 

2.32378 

2.32193 

185 

5  • 

925 

5 

2.32932 

2-32927 

—      5 

31A 

17 

6  |   2  .  33200 

2.32760 

—    44° 

2 

—    880 

~\  =  5-9589 


A 


—  0.00193 


.  e.  =        0.00016 


STAR  No.  377  /.  c.— (With  1032.) 


Date 

&JT-  *  ' 

log.r 

A 

P 

/A 

June    7 

8 

9 

12 

13 

2  .  83400 

2.83705 

+   0.00305 

i 

-f  0.00305 

14 

2.82985 

2.82736 

249 

3^ 

871 

19 

2  .  84207 

2.83701 

506 

3 

—        1518 

21 

2.83180 

2.82974 

206 

4 

824 

22 

2.83075 

2.82914 

161 

4 

644 

27 

2.83356 

2.83148 

—          208 

5 

—        1040 

28 

2-83035 

2  .  82600 

435 

2^ 

—       1087 

29 

2.82931 

2.82296 

635 

3^ 

—            2222 

30 

2.83107 

2.82425 

682 

4 

2728 

July    3 

2  .  82480 

2.82096 

384 

3 

—            H52 

4 

2  .  82968 

2  .  82900 

68 

4^ 

306 

5 

2  .  83608 

2.83298 

310 

4 

—            I24O 

6 

2.83912 

2.83265 

—          647 

2^ 

—            l6l7 

A    I     —  0.00336 


[p]  = 


—  6.2716 


p.  e.  = 


0.00028 


M.-P.— VOL.  I.]     CRAWFORD— CONSTANT  OF  REFRACTION.          l8l 
STAR  No.  377  /.  c.— (With  1156.) 


Date 

/qf.  *"  ' 

log.  r 

A 

/ 

/A 

June  7 

2.83328 

2.83115 

—  0.00213 

5 

—  0.01065 

8 

2.83152 

2.82838 

314 

4 

—   1256 

9 

2.83045 

2.82720 

325 

3 

—    975 

12 

13 

2  .  83400 

2.83306 

94 

% 

47 

14 

2.82985 

2  .  82607 

378 

3^ 

—    !323 

19 

2  .  84207 

2.83464 

743 

3 

—    2229 

21 

2.83180 

2  .  83048 

132 

4 

528 

22 

2.83075 

2  .  82840 

—    235 

4 

940 

27 

2.83356 

2.83081 

—    275 

5 

—    1375 

\j  i  \j 

28 

2.83035 

2  .  82647 

388 

3 

—    1164 

29 

2.82931 

2.82312 

619 

4 

—   2476 

30 

2.83107 

2.82833 

274 

4 

—    1096 

July  3 

2  .  82480 

2.82124 

356 

3 

—    1068 

4 

2.82968 

2  .  82730 

238 

5 

—    1190 

5 

2.83608 

2.83239 

369 

3^ 

—    1291 

6 

2.83912 

2  •  83502 

—    410 

2^ 

1025 

A      I      —  O.OQ334 


=  57  ;  log  [pvv]  =  6.0815 


STAR  No.  1156. 


p.  e.  =• 


0.00018 


Date 

£#•.  r  ' 

log.r 

A 

P 

/A 

June  7 

2.87524 

2.87330 

—  0.00194 

5 

—  0.00970 

8 

2.87296 

2.87010 

286 

4 

—   1144 

9 

2.87172 

2.86876 

296 

3 

—    888 

12 

13 

2-87557 

2.87471 

86 

tf 

43 

H 

2.87138 

2.86795 

343 

3^ 

1  200 

19 

2  .  88372 

2.87698 

674 

3 

—     2022 

21 

2.87302 

2.87182 

120 

4 

480 

22 

2.87193 

2  ..86980 

213 

4 

852 

27 

2  .  87448 

2.87197 

251 

5 

—     1255 

28 

2.87189 

2.86837 

352 

3 

—     1056 

29 

2  .  87078 

2.86516 

562 

4 

2248 

3° 

2  .  87246 

2.86996 

—      250 

4 

—     IOOO 

July  3 

2.86594 

2.86271 

323 

3 

969 

4 

2.87134 

2.86918 

216 

5 

—   1080 

5 

2-87773 

2.87437 

336 

3^ 

—   1176 

6 

2  .  88028 

2.87655 

—    373 

2^ 

—    .933 

=  57  ;  log  [pw}  =  6.0105 


I      —  0.00304 
p.  e.  =  it  0.00016 


182  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 

STAR  No.  1162.  — (With  406  /.  c.) 


Date 

/#£-.  r  ' 

log.  r 

A 

P 

/A 

June    7 

Q 

O 

9 

2.57666 

2-57349 

—  0.00317 

3/2 

—  0.01109 

12 

13 

2.57998 

2.57897 

IOI 

% 

50 

14 

2.57649 

2-57339 

310 

31A 

—       1085 

19 

2.58742 

2.58196 

546 

3               -        1638 

21 

2.57789 

2.57491 

298 

4 

—       1192 

22 

2.57681 

2-57474 

207 

4                           828 

27 

2.57924 

2.57728 

196 

5 

980 

28 

2.57699 

2-57364 

335 

3^     !      —        1173 

29 

2.57604 

2.57302 

302 

4 

—       1208 

3° 

2-57739 

2.57226 

513 

4 

—       2052 

July     3 

2-57156 

2.56791 

365 

3^ 

—       1277 

4 

2.57727 

2.57417 

310 

5 

—       1550 

5 

2.58212 

2.58006 

—          206 

3^                        72i 

6 

2.58448 

2.57905 

—          543 

3               —        l629 

—  0.00330 


=  50  ;  log  [pvv]  =  5.8169 


STAR  No.  1162— (With  444  /.  c.) 


P>  e.  =  ±  0.00015 


Date 

&£•.  r  ' 

log.r 

A 

P 

/A 

June    7 

8 

9 

2  .  57666 

2.57219 

—  0.00447 

31A 

—  0.01564 

12 

13 

2.57998 

2  .  57648 

350 

X 

175 

14 

2.57649 

2.57545 

104 

2^ 

260 

19 

2.58742 

2.58178 

564 

3 

—      1692 

21 

2.57789 

2.57518 

271 

4 

1084 

22 

2.57681 

2.57583 

98 

4 

392 

27 

2.57924 

2.57694 

230 

5 

—      1150 

28 

2.57699 

2.57306 

393 

4 

-       1572 

29 

2.57604 

2.57358 

246 

3/2 

86  1 

30 

2-57739 

2.57309 

430 

4 

—         1720 

J«ly    3 

2.57156 

2  -  56904 

252 

3 

756 

4 

2.57727 

2.57438 

289 

5 

—         H45 

5 

2.58212 

2.58035 

177 

3^ 

619 

6 

2.58448 

2  .  58043 

—          405 

2 

—          810 

v]  =  5-8851 


A     I     —  0.00297 
p.  e.  db  0.00017 


M.-P.—  VOL.  I.]      CRAWFORD-CONSTANT  OF  REFRACTION.         183 
STAR  No.  406  /.  c.— (With  1162.) 


Date 

/cg-.  r  ' 

log.r 

A 

P 

/A 

June    7 

Q 

O 

9 

2-59357 

2.59052 

—  0.00305 

3$ 

—  0.01067 

12 

13 

2.59683 

2.59586 

97 

l/2 

49 

14 

2.59350 

2.59052 

298 

3^ 

—         1043 

19 

2  .  60425 

2.59900 

—          525 

3 

—        1575 

2r 

2-59477 

2.59191 

—          286 

4 

—         H44 

22 

2.59366 

2.59i65 

2OI 

4 

804 

27 

2  .  59602 

2.59413 

I89 

5 

945 

28 

2.59420 

2.59097 

323 

3^ 

—         1130 

29 

2.59315 

2.59022 

293 

4 

—         1172 

30 

2.59432 

2-58939 

493 

4 

—        1972 

July    3 

2.58842 

2.58491 

—          35i 

3^ 

—        1229 

4 

2.59297 

2.58997 

300 

5 

—        1500 

5 

2.59909 

2.59711 

198 

3^ 

693 

6 

2.60148 

2.59625 

—          523 

3 

—        1569 

I     —  0.00318 


=  50  ;  log  [pvv}  =  5-7810 


STAR  No.  406  /.  c.— (With  1179.; 


P>  e-  =  db  0.00015 


Date 

/<£••  r  ' 

log.  r 

A 

P 

/A 

June  7 

2-59730 

2-59537     —  0.00193 

4 

•  —  0.00772 

8 

2.59456 

2.59219          237 

4 

948 

9 

2-59357 

2.59002     —    355 

4 

—   1420 

12 

13 

2.59683 

2.59691     +      8 

% 

+      4 

14 

2.59350 

2.59039          3ii 

4 

—   1244 

19 

2  .  60425 

2.60003          422 

3 

—    1266 

21 

2-59477 

2  .  59104          373 

4 

—    1492 

22 

2.59366 

2.59077          289 

4 

—    1156 

11 

2.59602 
2.59420 

2.59413 
2.59084 

I89 
336 

5 
3^ 

945 
—    1176 

29 

2.593r5 

2.59041 

274 

3l/2 

959 

30 

2.59432 

2  .  59002 

43° 

3*/2 

—    1505 

July  3 

2.58842 

2.58574 

268 

3/2 

938 

4 

2.59297 

2.59II2              185 

4^ 

832 

5 

2.59909 

2  .  59686              223 

4 

892 

6 

2  .  60148 

2  •  59683      —      465 

3 

—    1395 

A 


—  0.00292 


=  5-6978 


p.  e.  =• 


o.  oooi  i 


184  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 

STAR  No.  1179.— (With  406  /.  c.) 


Date 

log.  r  ' 

log.  r 

A 

P 

*>A 

June  7 

2.58409 

2.58211 

—  0.00198 

4 

—  0.00792 

8 

2.58167 

2.57922 

245 

4 

980 

9 

2-57955 

2.57590 

365 

4 

—   1460 

12 

13 

2.58282 

2  .  58290 

+      8 

% 

+      4 

14 

2  -  57953 

2.57633 

320 

4 

—    1280 

19 

2.59007 

2.58573 

434 

3 

1302 

21 

2.58069 

2.57682 

387 

4 

-    1548 

22 

2-57955 

2.5/657 

298 

4 

—    1192 

27 

2.58185 

2.57990 

!95 

5 

975 

28 

2.58049 

2.57703 

346 

3# 

—     I2II 

29 

2.57918 

2.57635 

283 

3^ 

991 

30 

2.58015 

2.57569 

446 

3^ 

—    1561 

July  3 

2.57417 

2.57142 

275 

3^ 

962 

4 

2.57852 

2.57661 

191 

4^ 

—    860 

5 

2.58493 

2.58263 

230 

4 

920 

6 

2.58735 

2.58255 

—    480 

3 

1440 

—  0.00301 


[p.  1  =  58  ;  log  [pvv}  =  5-7112 


STAR  No.  1179— (With  444  /.  £. 


Date 

log.  r  ' 

log.r 

A 

P 

/A 

June    7 

2.58409 

2-58351 

—  0.00058 

3 

—  0.00174 

8 

2.58167 

2.57807 

360 

4 

—       1440 

9 

2  -  57955 

2.57462 

493 

4 

—       1972 

12 

13 
14 

2.58282 
2-57953 

2.58043 
2-57837 

239 
116 

# 

3 

348 

19 

2.59007 

2  •  58554 

453 

3 

—       1359 

21 

2.58069 

2.57709 

360 

4 

—       1440 

22 

2  •  57955 

2  .  57766 

189 

4 

756 

27 

2.58185 

2.57956 

229 

5 

—       U45 

28 

2-58049 

2.57646 

—          403 

4 

—       1612 

29 

2.57918 

2  -  57692 

-          226 

3 

678 

3° 

2.58015 

2.57654 

361 

3/2 

1264 

July    3 

2.57417 

2.57254 

163 

3 

489 

4 

2-57852 

2.57681 

171 

*y* 

769 

5 

2-58493 

2.58293 

—          200 

4 

800 

6 

2-58735 

2  -  58392 

—          343 

2 

—          686 

=  54TA  ;  log[pvv]  =  5-9I25 


—  0.00276 


p.  e.  =  ±  0.00015 


M.-P.—  VOL,  I.]     CRAWFORD— CONSTANT  OF  REFRACTION.          185 
STAR  No.  1182. 


Date 

/£>£•.  r  ' 

log.r 

A 

P 

/A 

June  7 

.97645 

1-97543 

—  0.00102 

3 

—  0.00306 

8 

.97288 

1.97230 

58 

4 

232 

9 

.97180 

.96923 

257 

4 

—   1028 

12 

J3 

.97496 

.97520 

+       24 

2>^ 

+    60 

H 

.97208 

.97690 

482 

4 

1928 

19 

.98178 

.98268 

90 

3 

270 

21 

.97296 

•97359 

63 

4 

252 

22 

.97167 

.97248 

4-    81 

4 

+    324 

27 

.97413 

.97382 

31 

5 

155 

28 

.97291 

.97313 

+       22 

4 

+     88 

29 

•97153 

.97179 

+       26 

3 

+     78 

30 

.97242 

.97128 

114 

3/2 

399 

July  3 

1.96655 

.96918 

+      263 

3 

+    789 

4 

.97073 

•97058 

15 

5 

75 

5 

1.97694 

•97520 

174 

4 

696 

6 

1.97923 

.97855 

—     68 

3 

—    204 

OJ  =  59;  log  [pvv]  =  6.2272 


{-   O.OOOI2 


p.  e.  = 


0.00020 


STAR  No.  424  /.  c.— (With  1105.) 


Date 

log.r' 

log.  r 

A 

P 

/A 

June  7 

9 

1.97474 

1.97216 

—  0.00258 

31/* 

—  0.00903 

12 

13 

.97816 

•97571 

245 

2 

490 

14 

.97502 

.97941 

439 

3/2 

+   1536 

19 

.98471 

.98534 

+     63 

3 

1  80 

21 

.97609 

.97465 

144 

4 

576 

22 

•97473 

.97414 

59 

4 

236 

27 

.97727 

.97488 

239 

5 

—   1195 

28 

.97613 

.97658 

+     45 

3 

+    135 

29 

.97468 

.97465 

3 

3  , 

9 

3° 

•97549 

.97470 

79 

4/2 

356 

July  3 

.96971 

.97021 

+     5o 

3 

150 

4 

•97371 

•97437 

+     66 

5 

+    33° 

5 

.98000 

.97964 

36 

4 

144 

6 

•98238 

.98236 

—        2 

3 

—      6 

I     —  0.00031 


=  6.1588 


p.  e.  = 


0.00022 


1 86  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  3D  SER. 

STAR  No.  424  /.  c.  —  (With  1182.) 


Date 

/££-.  r  ' 

log.  r 

A 

P 

/A 

June  7 

1.97982 

.97882 

—  o.ooioo 

3 

—  0.00300 

8 

•97599 

•97534 

65 

4 

260 

9 

•97474 

.97220 

254 

4 

—    1016 

12 

13 

.97816 

.97841 

+   25 

2^ 

+     62 

14 

.97502 

.97982 

+   480 

4 

-f-    1920 

19 

.98471 

.98556 

85 

3 

255 

21 

.97609 

.97672 

63 

4 

+    252 

22 

•97473 

•97552 

+     79 

4 

4-    316 

27 

.97727 

•97695 

32 

5 

160 

28 

.97613 

•97635 

+       22 

4 

+    t-88 

29 

.97468 

•97493 

+       25 

3 

+     75 

30 

•97549 

•97433 

116 

31A 

—   T4o6 

July  3 

.96971 

.97225 

+    254 

3 

+    [762 

4 

•97371 

•97354 

17 

5 

85 

5 

1.98000 

.97823 

177 

4 

708 

6 

1.98238 

.98164 

—     74 

3 

—      222 

I       +  o.oooio 


=  59  ;  log  [pvv  ]  =  6. 2248 


STAR  No.  438  /.  c. 


p.  e.  = 


0.00020 


Date 

/<#•.  r  ' 

log.  r 

A 

/ 

/A 

June    7 

2  .  02896 

2.02882 

—  0.00014 

3 

—  0.00042 

8 

2.02529 

2.02288 

241 

4 

964 

9 

2  .  02369 

2.02263 

106 

4 

424 

12 

13 

2.02753 

2.02727 

—            26 

i# 

39 

M 

2.02398 

2.02841 

+          443 

2^ 

+        1107 

19 

2.03351 

2.03234 

117 

3 

35i 

21 

2  .  02530 

2  .  02690 

+           160 

4 

640 

22 

2.02385 

2.O242O 

+            35 

4 

+          HO 

27 

2  .  02640 

2.02592 

48 

5 

240 

28 

2.02535 

2.02702 

+           167 

4 

668 

29 

2  .  02403 

2.02415 

12 

3^ 

42 

30 

2  .  02436 

2.02547 

III 

4 

444 

July   3 

2.OI9OO 

2  .  02057 

157 

3 

471 

4 

2.O2276 

2.02333 

57 

5 

285 

5 

2.029T5 

2.02958 

43 

4 

172 

6 

2.03160 

2.03338 

+          178 

2 

+          356 

A 


-f  0.00040 


[p ]  =  56^  ;  log [fiw]  =  6.0647 


P.  e.  =  i  0.00017 


.:  I.]      CRAWFORD— CONSTANT  OF  REFRACTION.          187 
STAR  No.  444  /.  c—  (With  1162.) 


Date 

log.  r  ' 

log.  r 

A 

P 

/A 

June  7 

o 

9 

2.62193 

2.61791 

—  0.00402 

31A 

—  0.01407 

12 

T3 

2.62622 

2  .  62306 

316 

% 

158 

H 

2.62223 

2.62129 

94 

*X 

235 

!9 

,  2.63245 

2.62736 

509 

3 

—   1527 

21 

2,62367 

2.62123 

244 

4 

976 

22 

2.62220 

2.62132 

88 

4 

372 

27 

2.62478 

2.62271 

207 

5 

1035 

28 

2  .  62369 

2.62016 

353 

4 

1412 

29 

2.62213 

2.61992 

221 

ZY* 

774 

3° 

2.62278 

2.61891 

387 

4 

1548 

July  3 

2.61701 

2.61475 

226 

3 

678 

4 

2.62082 

2.61819 

263 

5 

1315 

5 

2.62782 

2.62622 

160 

3^ 

560 

6 

2.63053 

2.62688 

-    365 

2 

—    730 

=47%  I  log[pvv]  —  5-7941 


I     —  0.00268 


P.  e.  = 


0.00015 


STAR  No.  444  /.  c. — (With  1179.) 


Date 

log.  r  ' 

log.  r 

A 

P 

/A 

July  7 

2.62762 

2  .  62709 

-  0.00053 

3 

—  0.00159 

8 

2.62363 

2.62036 

327 

4 

1308 

9 

2.62193 

2.61745 

448 

4 

1792 

12 

13 

2.62622 

2.62405 

217 

% 

108 

14 

2.62223 

2.62118 

105 

3 

315 

19 

2.63245 

2.62834 

411 

3 

—    1233 

21 

2.62367 

2  .  62042 

325 

4 

22 

2.62220 

2.62048 

172 

4 

688 

27 

2.6-478 

2.62270 

208 

5 

1040 

28 

2.62369 

2  .  62003 

366 

4 

1464 

29 

2.62213 

2  .  62OO7 

206 

3 

618 

3° 

2.62278 

2.61950 

328 

2.Y* 

1148 

July  3 

2.61701 

2.61553 

148 

3 

444 

4 

2  .  62082 

2.61927 

155 

4^ 

698 

5 

2  .  62784 

2.62599 

185 

4 

740 

6 

2-63053 

2.62743 

—    3'Q 

2 

—    620 

A     |     —  0.00251 


;  log 


=  5-8266 


p.  e.  = 


0.00013 


1 88  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 

STAR  No.  1225. 


Date 

•^ 

log.  r 

A 

P 

/A 

June  7 

2.02116 

2.02103 

—  0.00013 

3 

—  0.00039 

8 

2.01757 

2.01515 

242 

4 

968 

9 

2.01589 

2.01481 

108 

4 

432 

12 

13 

2  .  O2OO4 

2.01978 

—     26 

il4 

39 

*4 

2.01668 

2.02119 

-f    45i 

2/4 

-f    1127 

J9 

2  .  02602 

2  .  02486 

116 

3 

348 

21 

2.01728 

2.01891 

+    163 

4 

-f    952 

22 

2.01609 

2.0I64I 

+     32 

4 

-f    128 

27 

2.01853 

2.01804 

-   46 

5 

230 

28 

2.01726 

2.01895 

+    169 

4 

+    676 

29 

2.01634 

2.01645 

+     ii 

3% 

39 

30 

2.01658 

2.01770 

-}-      112 

4 

448 

July  3 

2.0II55 

2.01322 

4-   167 

3 

SOT 

4 

2.01453 

2.0I5II 

58 

5 

290 

2.02135 

2.O2l8l 

+   46 

4 

184 

6 

2.02390   j    2.02576 

+    186 

2 

+    372 

I   +  0.00042 


=  6.0780 


p.  e.  = 


0.00018 


The  next  table  contains  the  results  collected  from  those 
preceding.  The  weights  given  in  the  column^  have  been 
derived  from  the  probable  errors  as  given  in  column  r. 
The  remaining  columns  are  self-explanatory. 


M.-P.— VOL.  I.]      CRA  WFORD-  CONSTANT  OF  REFRA  CT1ON. 


189 


Star 

A 

r 

log.  r2 

log.  p 

p 

PA 

948 

-  205 

±15 

2.3522 

1.0964 

12.5 

—  0.02562 

190  /.  c. 

—  513 

47 

3  3442 

0.1044 

!-3 

667 

959(D 

-  584 

53 

3.4486 

o.oooo 

1.0 

584 

9592) 

—  462 

27 

2.8627 

0.5859 

3-9 

—   1802 

968 

-f  662 

36 

3  .  i  i  26 

0.3360 

2.2 

+   1456 

977 

+  476 

40 

3.2041 

0.2445 

1.8 

+    857 

984 

—  142 

17 

2.4609 

0.9877 

9-7 

1377 

225(1)7.*. 

—  211 

15 

2.3522 

1.0964 

12.5 

2637 

225,2)  /.  c. 

—  126 

15 

2.3522 

1.0964 

!2-5 

1675 

225*3)  I-  C. 

997 

10051) 

-  159 
+  652 
—  215 

i 

21 

2.2279 
3.1126 
2.6444 

I  .  2207 

0.3360 

0.8042 

16.6 

2.2 

6.4 

—   2639 
+   1434 
1376 

1005(2, 

31 

19 

2-5575 

0.8911 

7-8 

242 

1009 
1019(1) 

+  298 
f  488 

38 
40 

3^596 
3  •  2041 

o  .  2890 

0.2445 

i.-9 

1.8 

+    566 
878 

1019:2) 

+  290 

38 

3-1596 

o  .  2890 

1-9 

+    551 

264  /.  c. 

—  218 

20 

2.6021 

0.8465 

7-o 

—    1526 

1032 

—  3*7 

29 

2  .  9248 

0.5238 

3-3 

1046 

282  /.  c. 

—  473 

27 

2.8627 

0.5859 

39 

—    1845 

1084 

—  101 

35 

3.0881 

0.3605 

2-3 

232 

1094 

-  104 

34 

3.0630 

0.3856 

2.4 

250 

1105 

—  29 

23 

2.7235 

0.7251 

5-3 

154 

I  IIO 

-  84 

18 

2.5105 

0.9381 

8.7 

73i 

349  l-  c- 

-  84 

18 

2.5105 

0.9381 

8-7 

73i 

356  /-  c. 

—  33 

19 

2-5575 

o  .  89  1  1 

7-8 

257 

H35 

—  193 

16 

2.4065 

I  .0421 

n  .0 

—    2123 

377d)  I.  c. 

-336 

28 

2-8943 

0.5543 

3-6 

—     1210 

377(2  I.e. 

—  334 

18 

2-5'o5 

0.9381 

8.7 

2906 

1156 

—  3°4 

16 

2.4065 

.0421 

II.  0 

3344 

Il62;i) 

-  33° 

15 

2.3522 

.0964 

12.5 

4125 

Il62(2) 

—  297 

17 

2  .  4609 

0.9877 

9-7 

—    2881 

406,,  /.  c. 

-318 

15 

2.3522 

.0964 

12.5 

3975 

406,2,  /.  c. 

—  292 

n 

2  .  0828 

.3658 

23.2 

6774 

ii79(D 

—  301 

n 

2.0828 

-3658 

23.2 

6983 

1  179  2) 

-276 

15 

2.3522 

.0964 

12.5 

3450 

1182 

+   12 

20 

2.  6O2I 

0.8465 

7-o 

+     84 

424(1)  /.  c. 

—   31 

22 

2.6848 

0.7638 

5-8 

180 

42412)  LJC. 

+   10 

20 

2.  6021 

0.8465 

7-o 

+     70 

438  /.  c. 

+   40 

17 

2.4609 

0.9877 

9-7 

+     388 

444D  /.  c. 

—  268 

15 

2.3522 

1.0964 

12.5 

—    3350 

444(2)  /.  c 

—  251 

13 

2.2279 

I  .  2207 

16.6 

—    4167 

1225 

+   42 

18 

2.5105 

0.9381 

8-7 

+     365 

A       I    —  0.00180 


=  340.6 


[pVV  ]   =  O.OO 

A  =  —  0.00180 


0.00019 


190  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 

4.  The  Constant  of  Refraction. — The  value  of  a  deduced 
by  Gylden  for  the  Pulkowa  Tables,  as  given  in  his  "Unter- 
suchungen  iiber  die  Constitution  der  Atmosphare  u.s.w.,"  is 

a  =0.00027985  =  57". 723. 
This  is  for  B  =  29.5966  inches  at  o°  and  /  ±=  7°. 44  R. 

The  Pulkowa  Tables  used  here,  however,  are  Gylden's 
with  JJL  systematically  reduced  by  —  0.00124.  Combining 
this  with  the  value  found  for  A«,  the  correction  to  Gylden's 
constant  becomes 


and  a  =      57".  548. 

This   reduced   to   the  condition  of  760  mm.  pressure  at  o° 
and  o°  C  temperature  gives 

a=       60".  159. 
To  this  value  of  a  correspond  the  following: 

c  =  0.00029182 
and  ^=1.00029178. 

For  the  sake  of  comparison,  the  most  important  deter- 
minations of  the  constant  of  refraction  are  given  below. 
These  values  are  for  the  conditions  B  =  760  mm.  at  o°  C 
and  external  thermometer  =  o°  C.  (These  values  are  taken 
from  Professor  Bauschinger's  * 'Untersuchungen  iiber  die 
Astronomische  Refraction  u.s.w."). 

a  /A 

1.  Fund.   Astr 60". 320  1.00029257 

2.  Tab    Reg 440  29315 

3.  Tab.  Pulk 268  29232 

4.  FuSS .122  29161 

5.  Greenw.  1857-1865 ..  .120  29160 

6.  Pulk.  1865 .209  29203 

7.  -Greenw.  1877-1886.  .  .192  29I95 

8.  Pulk.  1885 058  29130 

9.  Miinchen .104  29152 


M.-P.-VOL.  I.]      CRA  WFORD-  CONSTANT  OF  REFRA CTION. 


The  first  and  second  of  these  are  determinations  by 
Bessel;  the  third  by  Gylden;  the  fifth  by  Stone;  the 
sixth  by  Nyren;  the  seventh  by  Newcomb;  the  eighth  by 
Nyren;  and  the  last  by  Bauschinger. 

Bauschinger  gives  weight  zero  to  each  of  Bessel's 
determinations;  to  the  first,  because  there  was  considerable 
uncertainty  in  Bradley's  meteorological  instruments;  to  the 
second,  because  of  the  uncertainty  in  reading  the  Meridian 
Circle  (read  by  vernier  to  one  second).  He  gives  equal 
weight  to  the  last  seven,  and  gets  for  a  mean 

a  =  60".  1 53     and     i*>  =  1.00029176. 

5.  Latitude. — The  following  table  gives  the  value  of 
<f  deduced  separately  from  the  southern  and  from  the 
northern  stars.  All  of  the  stars  of  the  list  down  to 
84°  Z.  D.  were  used. 

V  --=  +  37°  20' 


Date 

V* 

P 

*fcs 

?N 

P 

P9x 

June    7 

25-38 

4 

101.52 

24.89 

4 

99.56 

8 

25-88 

4 

103-52 

24.71 

4 

98.84 

9 

26.49 

4 

105.96 

24.27 

4 

97.08 

12 

26.08 

i 

26.08 

24.96 

i 

24.96 

J3 

25-99 

2 

51-98 

25.27 

2 

50-54 

14 

25.88 

4 

103.52 

25.26 

3 

75.78 

19 

26.55 

4 

106.20 

24-54 

3 

73-62 

21 

25-99 

5 

129-95 

24.66 

4 

98.64, 

22 

25-65 

5 

128.25 

24-54 

4 

98.16 

27 

25-67 

7 

179.69 

24-59 

5^ 

135-24 

28 

26.48 

4 

105.92 

24.87 

3 

74.61 

29 

25.10 

5 

125-50 

24.89 

4 

99-56 

30 

26.08 

5  • 

130.40 

24.80 

4 

99.20 

July   3 

25.60 

4 

IO2  .  40 

24.91 

3 

74-73 

4 

26.03 

7 

182.21 

25.22 

5^ 

138.71 

5 

25-95 

5 

129.75 

25.07 

4 

100.28 

6 

26.80 

3 

80.40 

24.60 

3 

73-8o 

2        \     73 

I893-25 

61 

1513-31 

Weighted  mean  <p 

25-93 

24.81 

Applying  the  new  refractions  found   here,  the   latitudes 
become  from  the 

Southern  Stars  —  <p  =25''. 55 

Northern  Stars  —  <p  =  25  .19 
giving  for  the  mean  <p  at  this  epoch  (1899  June  22), 

f—  -4   37°  20'  25".37. 


192  CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 

The  remainder  of  the  difference  between  the  values  of  <p 
as  found  from  the  northern  stars  and  from  the  southern  stars 
(o".36)  is  probably  due  to  slight  errors  in  the  declinations 
of  the  stars  used,  and  to  bisection  error. 

CONCLUSION. 

In  conclusion  it  is  desired  to  state  that  limitations  of  time 
have  prevented  the  complete  reduction  of  these  observations 
and  of  the  series  taken  during  the  fall  months  (1899 
Oct. -Dec.).  It  is  hoped  that,  in  the  near  future,  time  will 
be  available  in  which  to  carry  out  these  reductions  by 
correcting  the  declinations  used  and  then  repeating  such 
portions  of  these  computations  as  will  be  necessary.  It  is 
also  desired  to  make  reductions  which  will  include  the 
relative  humidity  and  a  term  depending  upon  the  zenith 
distance. 

It  will  be  noticed  from  the  table  (p.  189)  that  there  is  a 
large  range  in  the  values  of  A>  viz.,  from  —  0.00584  to 
-f-  0.00662.  This  discordance  is  due  partly  to  the  values  of 
the  declinations  adopted,  but  is  also  very  clearly  a  function 
of  the  zenith  distance.  By  introducing  a  term  depending 
upon  the  zenith  distance,  and  re-solving  by  Least  Squares, 
this  discordance  can  be  greatly  diminished. 

From  this  investigation  the  following  conclusions  can  be 
drawn:  — 

1 .  That  this  preliminary  reduction  gives  for  the  Constant 
of   Refraction 

a  =  60".  159 
for  B  =  760  mm.  at  o°  (C)  and  /  =  o°  (C). 

2.  That  for  the  epoch  1899  June  22,  the  latitude  of  the 
Lick  Observatory  Meridian  Circle  was 

v  =  +  37°  20'  25".37. 

3.  That  the  final  reduction  will  show  that  the  Constant 
of  Refraction  of  the  Pulkowa  Tables  is  too  large. 

4.  That  the  observing  room  of    the    Lick  Observatory 
Meridian  Circle  is  of  a  very  good  design,  and  that  there  is 
no  need  of  mounting  Meridian  Circles  in  the  open  air. 


M.-P.—  VOL.  I.]      CRAWFORD—  CONSTANT  OF  REFRACTION.         193 

ADDENDUM. 

The  table  on  page  189  shows  a  large  range  in  the  values 
of  A,  viz.,  from  -{-0.00662  to  —  0.00584.  Upon  plotting 
these  values,  using  the  zenith  distance  z  for  abscissa,  and 
A  for  ordinate,  it  is  easily  seen  that  A  varies  quite  uniform- 
ally  with  the  zenith  distance.  A  straight  line,  inclined 
about  145°  to  the  zenith  distance  axis,  and  cutting'it  at  z  = 
about  55°,  appears  to  represent  A  very  well.  Therefore, 
assuming  Z  to  be  the  zenith  distance  for  A  =  o,  we  can  set 
up  an  observation  equation  of  the  following  type  for  every 
star  : 

loga=loga0-[-  [Z—  z]x, 

or 

loga  —  Ioga0  =  A  =  Zx  —  zx=  D  —  zx  , 
where 


and  where  a0  is  the  a  of  the  tables  used  (Pulkowa). 

Equations  of    this    kind  were,  accordingly,  formed    and 
solved  for  Z  and  x  by  the  method  of  Least  Squares. 


CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  30  SER. 

Equations  of  Condition. 


=    — zx. 


No. 

Star 

D    —     zx 

A 

P 

i 

948 

D        80.00  x 

=  —o  .  00205 

12.5 

2 

190  1.  e. 

89.20 

—  —   513 

3 

959 

88.76 

=  -  487 

4-9 

4 

968 

30-38 

=  4-   662 

2.2 

5 

977 

21-55 

=  4-   476 

1.8 

6 

984 

78.11 

=  —   142 

9-7 

7 

225  1.  c. 

79.70 

=  —   167 

41.6 

8 

997 

30-59 

=  +   652 

2.2 

9 

1005 

57-J9 

=  —   114 

14.2 

10 

1009 

21.34 

=  +   298 

ii 

1019 

21-49 

=  +   386 

3-7 

12 

264  I.e. 

57-35 

=  —   218 

7.0 

13 

IO}2 

87.05 

=  —   317 

3-3 

14 

282  1.  c. 

88.67 

=  —    473 

3-9 

15 

1084 

27.80 

=  —    101 

2-3 

16 

1094 

28.49 

=  —    104 

2.4 

17 

1105 

62.21 

=  —    29 

5  3 

18 

IIIO 

—    67.08 

84 

8.7 

19 

349  I-  c. 

67.65 

=  -    84 

8.7 

20 

356  1.  c. 

57-49 

33 

7-3 

21 

H35 

77-37 

=  —    193 

II.  0 

22 

377  Lc. 

86.79 

=  —   335 

12/3 

23 

1156 

87.23 

=  —   304 

II  0 

24 

1162 

83.21 

22.2 

25 

406  1.  c. 

83-50 

=  —   301 

35-7 

26 

1179 

—    83.26 

292 

35-7 

27 

1182 

62.79 

12 

7.0 

28 

424  1.  c. 

62.96 

9 

12.8 

29 

438  1.  c. 

65-52 

=  4-   40 

9-7 

30 

444  1.  c. 

83  99 

=  -   258 

29.  i 

31 

1225 

65-13 

=  4-   42 

8-7 

To  reduce  the  number  of  equations,  those  nearly  alike 
were  combined,  as  follows:  Equations  No.  i,  6,  7  and  21; 
2,  3  and  14;  4  and  8;  5,  10  and  n  ;  9,  12  and  20;  13,  22 
and  23;  15  and  16;  17,  27  and  28;  18  and  19;  24,  25,  26 
and  30;  and  29  and  31,  giving  the  n  equations:  — 


No. 

i 

2 

3 


9 
10 
ii 


79.20 
8S.78 
30.48 
21.47 

57-31 
87.03 

27-I5 
62  75 
67.36 
83  49 
65.34 


x       = 


I 


i 

P 

.00174 

74.8 

485 

IO.  I 

657 

4-4 

385 

7-4 

117 

29.0 

320 

26.6 

I03 

4-7 

7 

25.1 

84 

17.4 

291 

122.7 

18.4 

8.6 
3  2 

2.  I 
2.7 

5-4 
5-2 

2.2 

50 

4.2 

II. I 

4-3 


M.-P.-VoL.  I.]     CRAWFORD-CONSTANT  OF  REFRACTION.          195 
Weighted   Observation  Equations. 


fo. 

a 

b 

n 

I 

8.6  D  — 

681.1  x 

= 

—  0.01496 

2 

3-2 

284.1 

=: 

—   1552 

3 

2.1 

57  9 

= 

+   1248 

4 

2-7 

58.0 

= 

-j-   1040 

5 

5-4 

309-5 

= 

-   632 

6 

5-2 

452-4 

S= 

1664 

7 

2.2        — 

59-7 

= 

227 

8 

50 

3I3-7 

= 

35 

9 

4-2 

282.9 

= 

—    353 

10 

II  .  I 

926.7 

t= 

-   3230 

ii 

4-3 

281.0 

== 

+    176 

;  .       ;  -  '     .      ,  '  •         'V   i  -  ' 

To  render  these  more  nearly  homogeneous,  let  D=D; 
loox—  y  and  multiply  the  absolute  term  by  100.  Then  we 
have  the  following 

Weighted  Homogeneous   Observation  Equations. 


Vo. 

a 

b           n 

i 

8.6  D 

6.811 

y  =  '  • 

1.496 

2 

3-2 

2.841 

—  — 

1-552 

3 

2.  [ 

o  579 

—  i 

1.248 

4 

2-7 

0.580 

—  _|_ 

i  .040 

5 

54 

3  095 

=  — 

O.6}2 

6 

5-2 

4-524 

—  — 

1.664 

7 

2.2      .  — 

0-597 

=  — 

0.227 

8 

5-o 

3-137 

=  — 

0.035 

9 

4.2 

2.829 

=  — 

o-353 

10 

II.  I 

9.267 

=;  — 

3-230 

ii 

4  3 

2  8lO 

-  + 

0.176 

Combining  these    by  the  method  of   Least  Squares  we 
obtain  the  following 

Normal  Equations. 
+  341.28  D  —  254.512  y=  —  61.7188 
—  254-51      -fipV-JS1     —-f53-4383 

Solving  these,  remembering  that  the  absolute  terms  had 
been  multiplied  by  100,  we  have 

log  0  —  7.75694;  log  y=8.  00376  or  log  x=6.  00376. 

Now  since  D=Zx,  we  have  log  Z  =  1.75318, 
Whence        x=  -{-0.0001009  and  Z=56 


Substituting  the  values  of  D  and  x,  thus   found,  in   the 
Weighted      Observation      Equations,     we     find      \_pw~\  = 


196  i    CALIFORNIA  ACADEMY  OF  SCIENCES.        [PROC.  3D  SER. 

0.00024690,  from  v^hjch  the  following  probable  errors  have 
been  deduced: 

^  <S  V.  v/. 

rx=,^f 0.0000130  and  r    =  ±0^031  =  ±o°i'52". 

*?.V  • 

We,  ther^fbrej  have  from  this  solution 

Z=56°38'.8±i'.9  and' x—+o.oooioi  ±0.000013, 
giving 

loga=loga0-\- o.oooioi  [56°38'.8 — z] . 

We  are,;therefore,  led  to  the  conclusion  that  the  so-called 
Constant  of  Refraction  needs  not  only  a  correction,  but  a 
Correction  for 'every  zenith  distance.  In  other  words,  the 
formula  from  which  refractions  are  computed  needs  to  be 
modified.  Or,  the  formula  may  be  retained  unaltered,  and 
the  desire^  result  pbtained  by  correcting  the  log  p  table  of 
the  refraction  tables  used  (Pulkowa)  by  the  amount 

A  log/*=p;oopioi  [56038'.8— z]. 

R.  T.  C. 


ranTcrd-     

Determination  of  the 
onstant  o:?  refraction 


YD  04994 


